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00:00:00Jai Hind friends, welcome to your own family. How are you all? Tell me. Is the audio and video clear? Tell me.
00:00:25All okay? Good evening, good evening, good evening to everyone. Ram Ram, Ram Ram, Radhe Radhe.
00:00:37Okay, very good. Everyone is live. Very well. Very good, brother.
00:00:42Okay, let's go, friends. So when everyone is live, let's talk further, my brother, and let's read the question ahead.
00:00:52When will the English medium of Railway Maths come?
00:00:55So, the 100-year engine will take a little time. It may take a month now.
00:01:01Within a month, the book will come in English and you will get it at all the shops.
00:01:06Okay?
00:01:08Let's go. Very good.
00:01:10So you will get the book of Railway Maths in English. It will take a little time.
00:01:14Come.
00:01:16Hello, brother. Hello to everyone. Hello.
00:01:19Let's go. Har Har Mahadev. Very good, brother.
00:01:22So tell me, how did you like tomorrow's class? Did you understand? Did you get clarity in a good way?
00:01:27Okay. We also have a reminder sheet for you.
00:01:31And in this, we have made you ask all the questions.
00:01:33Okay.
00:01:35Now look, I want to give you a little information.
00:01:38Actually, in the reminder, I have put 63 questions in it.
00:01:43And in reality, if we see, there should not be less than 100 questions.
00:01:47Okay. So here you will feel that why did the number of questions reduce?
00:01:51Why is it that the number of questions in them is less?
00:01:55So the reason I tell you is that I have transferred the questions of this to your second topic, i.e. HCF and LCM.
00:02:03Like every teacher has his own way of teaching.
00:02:06Someone, my brother, teaches the mixture allegation in the mixture itself and teaches the allegation separately.
00:02:11And some people combine both and go. Like I teach both separately.
00:02:15If you look at my mixture, you will get different questions. If you look at the allegation, you will get different questions.
00:02:19Many people teach the profit-loss discount at the same place. We teach profit-loss separately.
00:02:24We teach discount separately.
00:02:26We teach time and work separately. So we teach work and wage separately.
00:02:29Similarly, the questions of the reminder.
00:02:30Now, in reality, there is such a number in it that it is very difficult to get the LCM out.
00:02:35So first you have to learn how to get the LCM out.
00:02:40And then after that, you will solve those questions here.
00:02:43So the 30 to 40% question of the reminder, you will get to see it in HCF LCM.
00:02:49HCF LCM, my brother, is inside the topic here.
00:02:52Like here, the two concepts I taught you yesterday.
00:02:55Concept of same reminder, concept of difference.
00:02:57Same difference.
00:02:59Both of these, my brother, are here.
00:03:02I made you do the questions of this in your sheet yesterday.
00:03:05There are many questions of this that you will get to see in HCF LCM.
00:03:09Like if I read the question number now, when you look at the answer sheet of HCF LCM,
00:03:14So where are the same reminder questions in HCF LCM?
00:03:17I will give you a little idea here.
00:03:19Okay, because first I will teach you those things.
00:03:22After that, I will ask those questions here.
00:03:24Okay.
00:03:26So if you look here like this, then the question number is 52.
00:03:29My brother is 53.
00:03:31Here is the question number 54.
00:03:34HCF LCM, let X be the greatest number, which one divided by 955.
00:03:39This much reminder is going to be the same in every case.
00:03:42So what will we do?
00:03:44So there are many such questions, 55, 56, 57, 58.
00:03:47And this is my brother, which is a very good question.
00:03:50Where the questions are given to you in total.
00:03:52Now there are a total of four varieties in this.
00:03:55And we will discuss all four varieties.
00:03:57What happens in all four varieties?
00:03:59So the first discussion here is this.
00:04:01Find out the number that is being divided.
00:04:04Okay, so this is my brother, variety number one.
00:04:07And the second one is my brother, find out the number that is being divided.
00:04:11One that is being divided, we call it N.
00:04:14And the one that is being divided, we call it D.
00:04:17So my brother, two cases are made to find out N.
00:04:19A case of same reminder is made.
00:04:21And a case of our same difference is made.
00:04:24Similarly, D has to be found.
00:04:26Many times it will give different numbers.
00:04:28It will say that it has been divided by D.
00:04:30Same reminder is coming.
00:04:32So what will be the value of that D?
00:04:34And here too, my brother, the same difference is coming.
00:04:36So what will be the value of that D?
00:04:38We will go through this again in detail.
00:04:40We will tell you things in a good way.
00:04:43So for now, let's talk here.
00:04:45And here we understand things.
00:04:47See what has been said.
00:04:49So like the case of same reminder, we told you.
00:04:52That if you want to find that number, then take the LCM and add the reminder.
00:04:56Here too, if you want to find that number, then take the LCM and reduce the difference.
00:04:59On top of this, I also made you practice the question.
00:05:02If you know, then the question number was 25.
00:05:07It was above that.
00:05:09The question number was 27.
00:05:11It was above that.
00:05:13It was above the same difference, my brother.
00:05:15Did you understand here?
00:05:16Come here, my brother.
00:05:18After question number 25 and 27, here is question number 26.
00:05:21In the same way, it has also been given here.
00:05:23When a positive integer n is divided by 16, 17 and 18, leaves a remainder of 6, 7 and 8.
00:05:29If we look here, then there is a number of n there.
00:05:32In the same way, there is a number of n there.
00:05:35When divided by 16, how much is our remainder?
00:05:39So our remainder is 6.
00:05:41The same number of n is divided by 6, 7 and 8.
00:05:46When divided by 16, what is the story?
00:05:49When divided by 17, what is the story?
00:05:51And when divided by 18, what is our story?
00:05:54In this case, our remainder is 6.
00:05:56Here is 7 and here is 8.
00:05:59Now if you look here, then the remainder is different.
00:06:03So the remainder is different.
00:06:05So it doesn't matter.
00:06:07My eye is on the difference.
00:06:08So if I look at the difference here, then the difference between 16 and 6 is 10.
00:06:13The difference between 17 and 7 is 10.
00:06:17If you look here, then the difference between 18 and 8 is 10.
00:06:21So our difference is the same.
00:06:24So if I have to find that number, then I will take the LCM here.
00:06:30Whose 16, 17 and 18?
00:06:3316, 17 and 18.
00:06:35And after that, I will subtract from it.
00:06:38So here I will subtract the difference.
00:06:40So we will get that number.
00:06:43Now if we talk about that number, then 16 and 17.
00:06:46How much will it be?
00:06:48So 6 times 17.
00:06:502 times 102.
00:06:52And here it will be 272.
00:06:54And its 2 has come to us.
00:06:57What has not come is 9.
00:06:59So here 9 into 2 is 18.
00:07:0163 and 64.
00:07:03And my brother is 24 here.
00:07:05So how much will it be?
00:07:07248.
00:07:09So how much is their LCM?
00:07:11So you will say 248.
00:07:13What is our difference?
00:07:15If it is 10, then we will subtract this difference.
00:07:17So it will be 2438 here.
00:07:19This will be our number.
00:07:21Today if we talk in this question.
00:07:23So here we have been told in the question.
00:07:26Find the remainder when it is divided by 11.
00:07:29Find the remainder here.
00:07:31When n square plus 5n plus 6.
00:07:33If we divide it here.
00:07:35So we divide it by 11 here.
00:07:38That is, somewhere we have to tell.
00:07:40See n square.
00:07:42What will happen to n square here?
00:07:442438.
00:07:46Divide the whole square of this number by whom?
00:07:48Plus my brother.
00:07:50How much will be 5 into?
00:07:52It will be 2438.
00:07:54Plus how much will be ours?
00:07:56So 6.
00:07:57So n square plus 5n plus 6.
00:07:59This has to be divided by whom?
00:08:01This has to be divided by 11.
00:08:03So when this 11 will divide it.
00:08:05So when this 11 will divide it.
00:08:07So from 11 you see here.
00:08:09One is that we solve the whole God.
00:08:11And then divide it by 11.
00:08:13I have always taught that first divide it.
00:08:15Then my brother solve it.
00:08:17First divide it.
00:08:19Then solve it.
00:08:21So if we see here.
00:08:23So what will we do first?
00:08:25We will divide it by 11 and see the remainder.
00:08:27We will divide it by 11 and see the remainder.
00:08:29So if you see from 11.
00:08:31So 11 times 2 is 22.
00:08:33Then 23 will come.
00:08:3511 times 2 is 22.
00:08:37Then after that it will be 18.
00:08:3911 times 1 is 18.
00:08:41How much will be the remainder?
00:08:437.
00:08:45I am repeating again.
00:08:47See, divide by 11.
00:08:492 times 22 is 23.
00:08:512 times 22 is 18.
00:08:531 time 11 is 7.
00:08:55Similarly, when you divide here.
00:08:57How much will be the remainder?
00:08:5949.
00:09:01After that 5 times 7 is 35.
00:09:03And how much will be the plus?
00:09:056.
00:09:07Divide by 11.
00:09:0949 and 6 is 55.
00:09:1155 and 35 is 90.
00:09:13And when we divide 90 by 11.
00:09:15How much will be the remainder?
00:09:172.
00:09:19Which option is correct?
00:09:21Option number B is correct.
00:09:23There is no problem.
00:09:25So keep this small thing in mind.
00:09:27When it comes to the same difference.
00:09:29Then take out the LCM and reduce the difference.
00:09:32So if you see here.
00:09:34We have only done the solution in this much.
00:09:36This was my way of explaining.
00:09:38That you take the LCM of these people here.
00:09:40Minus the difference from it.
00:09:42So this LCM came.
00:09:44Now the same number square plus the number of 5 times plus 6.
00:09:46All of them have to be divided by 11.
00:09:48So before 11, divide this, 7 will come.
00:09:50Divide this, 7 will come.
00:09:52By doing this, my brother.
00:09:54Do not multiply.
00:09:55For example, it is better to multiply the number and divide it.
00:09:57First divide it and then multiply it.
00:09:59Take out the remainders first.
00:10:01Like if you divide it, the remainder comes together.
00:10:03So instead of squaring the number.
00:10:05Square the remainder.
00:10:07If you divide it, my brother, 7 came.
00:10:09So 7 came.
00:10:11So my brother, instead of multiplying the number.
00:10:13Multiply the remainder.
00:10:15And do this.
00:10:17If you wanted this, you could have done it here too.
00:10:194 times 11 is 44.
00:10:215 will be left.
00:10:233 times 33, 2 will be left.
00:10:25There are small numbers here.
00:10:27So let's do one thing.
00:10:29We will divide it by adding it.
00:10:31That will be better.
00:10:33Let's go.
00:10:35I understood the thing here.
00:10:372438 will have a remainder of 8.
00:10:39Where will the remainder come from?
00:10:41You divide 2438 once and see.
00:10:43Where is 8 coming from?
00:10:45Okay, divide it once and see here.
00:10:47Take my brother, divide 2438 a little from 11.
00:10:49From which angle is your 8 coming?
00:10:51My brother became 22 in 2 times.
00:10:532 and 3 are left.
00:10:551 and 8 are left.
00:10:5711 in 1 time.
00:10:597 is left.
00:11:01So where is your remainder coming from?
00:11:03Tell me.
00:11:05Okay, see now the website is not working for us.
00:11:07So don't worry about the first thing.
00:11:09And the second thing is that my brother is not working here.
00:11:11So it will take 2-3 days to work on the test.
00:11:13So don't worry about that too.
00:11:15We are working on it too.
00:11:17So don't worry about the Aadarsh Chaudhary test.
00:11:19There is some technical glitch in the test for you.
00:11:21So in the future, do not worry about this.
00:11:22Whenever such questions come,
00:11:24then how to make it here.
00:11:26Okay, now let's go ahead
00:11:28and let's see what is said in the next questions.
00:11:30Okay, now see here.
00:11:32This is a little bit of our different question.
00:11:34We will also go on top of that.
00:11:36But here is a question from my side.
00:11:38You see here.
00:11:40How is it?
00:11:42What is it?
00:11:44Sir, how do you take 16, 17, 18 calcium?
00:11:46Tell me.
00:11:48Dude, Ankit Verma, tell me this too.
00:11:50It is a matter of common sense.
00:11:52This is the way.
00:11:54Although we will teach in LCMHCF.
00:11:56This is 16, this is 17, this is 18.
00:11:58You see here.
00:12:00Divide by 2.
00:12:02How many times?
00:12:048 times.
00:12:06This part will not happen.
00:12:08And how many times will this happen?
00:12:109 times.
00:12:12After that, no such number will be common.
00:12:14Which my brother divides all three here.
00:12:16So what does LCM mean here?
00:12:18LCM means 2.
00:12:19This is LCM.
00:12:21Ankit Verma, this is LCM.
00:12:23What else is LCM?
00:12:25Tell me.
00:12:27So this is our LCM here.
00:12:29Did you understand?
00:12:31Yes, let's go.
00:12:33Now let's see our next part.
00:12:35And which part we have solved here,
00:12:37I am telling you.
00:12:39And which part to see now,
00:12:41I will tell you.
00:12:43You have seen this story of the same difference.
00:12:45If our difference is the same
00:12:47after dividing by different numbers,
00:12:49then how will you make it?
00:12:51Like I have a simple question here.
00:12:53And in the question,
00:12:55my brother,
00:12:57this is my question here.
00:12:59Like it was said in the question
00:13:01that there is a number called n.
00:13:03If you divide it by 10,
00:13:05then how much is your remainder?
00:13:07Then your remainder is 2.
00:13:09If you divide it by 11,
00:13:11then also your remainder is 2.
00:13:13So what is the value of n?
00:13:15First question my brother here.
00:13:17After that, what will be the second question here?
00:13:19Here it is said that
00:13:21if you divide it by 10,
00:13:23then your remainder is 3.
00:13:25Or if you divide it by 10,
00:13:27if you divide it by 6,
00:13:29then your remainder is 3.
00:13:31If you divide it by 7,
00:13:33then also your remainder is 3.
00:13:35And if you divide n by 8,
00:13:37then also your remainder is 3.
00:13:39What is the smallest part of n?
00:13:41I have given you two questions.
00:13:43And here you have to answer both the questions.
00:13:45And which question is this,
00:13:47my brother?
00:13:50You make it.
00:13:52Whose question is this, my brother?
00:13:54It is the question of the same remainder.
00:13:56Sir, the class of remainder is not visible.
00:13:58Why? So whose class is visible, Kiran Chaudhary?
00:14:00Tell me, the class of remainder is visible.
00:14:02Tell me here.
00:14:04And whose class is visible?
00:14:06Amankumar, why don't you read my comment?
00:14:08Brother, tell me one thing,
00:14:10should I teach or should I read your comment?
00:14:12Tell me, my brother.
00:14:13Keep it with you.
00:14:15Let's go.
00:14:17A lot of people are giving answers here.
00:14:19See what is being said here.
00:14:21So here in the question,
00:14:23my brother, see
00:14:25what is to be done here first.
00:14:27So we will say,
00:14:29sir, what is here is LCM.
00:14:31The first thing we will do here
00:14:33is take LCM.
00:14:35Whose will we take?
00:14:3710 and 11.
00:14:39So whenever we have to find the number here,
00:14:41like if we take the numerator of n,
00:14:43then we are going to take LCM.
00:14:45Whose are we going to take?
00:14:47We are going to take 10 and 11.
00:14:49And after that,
00:14:51what we will do here is,
00:14:53we will add.
00:14:55And what will we add?
00:14:57We will add the remainder.
00:14:59So here you will say,
00:15:01sir, 10 and 11's LCM is 110.
00:15:03And if you add 2 in 110,
00:15:05then this will become 112.
00:15:07And this will be our correct answer.
00:15:09So what will be the answer of the first one?
00:15:11So we will say, sir, it will be 112.
00:15:13So what we do here is,
00:15:15we add.
00:15:17What do we do here in the same remainder?
00:15:19We add.
00:15:21Please keep this in mind.
00:15:23Okay.
00:15:25If we talk here,
00:15:27then what will be the story here?
00:15:29If we look here too,
00:15:31then we will say,
00:15:33sir, what will be the value of n?
00:15:35So in the same way,
00:15:37we will take LCM here.
00:15:39Whose 6, 7, 8.
00:15:41So here we will say,
00:15:43what will be the LCM of 6, 7, 8?
00:15:45My brother, 6 and 8's LCM is 24.
00:15:47Now see here,
00:15:49what will be the LCM of 6, 7, 8?
00:15:51So if you want like kids here,
00:15:53you can solve it like this,
00:15:55that 6, 7, 8,
00:15:57first we will divide by 2,
00:15:59it will go in 3 times,
00:16:01it will not be cut,
00:16:03it will go in 4 times.
00:16:05Now here it will not be cut from anyone,
00:16:074 into 7, 28 into 3, 84.
00:16:09Okay.
00:16:11Or 4 into 3, 12, 7, 84,
00:16:13whose LCM will come?
00:16:15It will come 176.
00:16:17And how much is the remainder?
00:16:19It is 3.
00:16:21So how much will 176 be?
00:16:23It will be 179.
00:16:25How much will it be here?
00:16:27179.
00:16:29Why is everyone getting different answers?
00:16:31Why didn't anyone get the answer 179?
00:16:333 of 84.
00:16:35One second,
00:16:37have we taken the wrong LCM?
00:16:40It is correct,
00:16:417 into 3, 21, 21,
00:16:43which is 84.
00:16:4584 will be 2 times,
00:16:47it will be 178.
00:16:49Look at the LCM here,
00:16:512 into,
00:16:53it will be 84.
00:16:55It will be 168.
00:16:57The LCM will be 168.
00:16:59How much will the LCM be?
00:17:01It will be 168.
00:17:03And in 168,
00:17:05we will add 3 remainders,
00:17:07how much will be the answer?
00:17:09It will be 171.
00:17:11The question is,
00:17:13whenever we divide by different numbers,
00:17:15but if the remainder is the same,
00:17:17the remainder is the same,
00:17:19then how do we find the number?
00:17:21We take the LCM of these numbers
00:17:23and add the remainder.
00:17:25You can ask one more question on this,
00:17:27so that it is clear.
00:17:29The number is n,
00:17:31we have to divide by 4.
00:17:33The remainder is 1.
00:17:35The number is n,
00:17:37we have to divide by 5.
00:17:39We have to divide by 5.
00:17:41The number is n,
00:17:43we have to divide by 7.
00:17:45The remainder is 1.
00:17:47There are many such questions,
00:17:49but the smallest one,
00:17:51you tell me here,
00:17:53that the smallest possible value here,
00:17:55how much will it be?
00:17:57There are many such questions in the remainder,
00:17:59which we will get self-made,
00:18:01which we will get ourselves,
00:18:03which will not be given in your sheet.
00:18:05So you have to practice on them.
00:18:07Like these same remainder questions are not here,
00:18:09these are given in the LCM,
00:18:11so that no concept is left out,
00:18:13nor is it less,
00:18:15and you can study here in a good way.
00:18:17Okay?
00:18:19Let's go.
00:18:21So if we look here,
00:18:23what will we say here?
00:18:25So we will say a small thing here.
00:18:27Guruji, it is a simple thing,
00:18:29if you want to find the value of n,
00:18:31take the LCM.
00:18:33Whose is 4, 5 and 7?
00:18:35So here 4, then 5, then 7.
00:18:37And what do you add in it?
00:18:39So add the remainder.
00:18:41So how much is 7 times 20 and 20?
00:18:43It is 140.
00:18:45How much is the remainder?
00:18:47It is 1.
00:18:49So my brother, what will be the answer?
00:18:51It will be 141.
00:18:53So there will be no problem here.
00:18:55Everyone can give the answer that it will be 141.
00:18:57So you will say, Guruji, yes.
00:18:59Okay?
00:19:01Now look here, my brother,
00:19:03what are the overall cases made here?
00:19:05And how do you have to tackle?
00:19:07The whole flowchart,
00:19:09this is my brother,
00:19:11what happens in the number system?
00:19:13Basically, there are two things here.
00:19:15One, my brother,
00:19:17is to find out what your n is.
00:19:20And the second, my brother,
00:19:22which is D here,
00:19:24from which you divide,
00:19:26my brother, find out what is here.
00:19:28Like the concept you have studied,
00:19:30what is it?
00:19:32That we divide n by D here,
00:19:34so here comes a remainder called r.
00:19:36So what were you studying so far?
00:19:38Find out that number.
00:19:39The same concept is made here,
00:19:41find out n.
00:19:43Now you will read further,
00:19:45what is the meaning of D here?
00:19:47Now you have seen two cases in n.
00:19:49What did you see in n?
00:19:51So you saw a case of the same remainder here.
00:19:53If we divide,
00:19:55we will have the same remainder.
00:19:57And what did you see here, my brother?
00:19:59So you saw the same difference.
00:20:01What did you see here, my brother?
00:20:03So you saw the same difference.
00:20:05Similarly, if we talk here, my brother,
00:20:07so what happens here in the case of D?
00:20:09Suppose you divide the numbers,
00:20:11so here too,
00:20:13the same story will be made here.
00:20:15Okay, I will copy it for you,
00:20:17and tell you the same thing here.
00:20:19Here too, both the cases will be made.
00:20:21The same remainder here,
00:20:23and the same difference here.
00:20:25That's why I said in the beginning,
00:20:27there are four types of cases.
00:20:29Case number 1, case number 2,
00:20:31case number 3, case number 4.
00:20:33Two cases are made to find n,
00:20:35and two cases are made here to find D.
00:20:37Do you understand what I am saying?
00:20:39So here it happens,
00:20:41find that number,
00:20:43find that number which is divided,
00:20:45and gives the same remainder.
00:20:47The second case,
00:20:49find that number which is divided,
00:20:51but gives the same difference.
00:20:53As you saw in this,
00:20:55suppose here is n,
00:20:57if we divide by 4,
00:20:59how much is the remainder? 1.
00:21:01The number is n,
00:21:03if we divide by 5,
00:21:05how much is the remainder? 1.
00:21:07So in the same situation,
00:21:09if we divide by 4,
00:21:11how much is the remainder? 4.
00:21:13If we divide by 5,
00:21:15how much is the remainder? 1.
00:21:17So this is the structure,
00:21:19without any problem.
00:21:21So this is the structure,
00:21:23without any problem.
00:21:25So this is the structure,
00:21:27without any problem.
00:21:29When the same remainder is there,
00:21:31what do we do by taking the maximum of the numbers?
00:21:33We add the remainder here.
00:21:35Now we will explain the second case,
00:21:37and the same difference here.
00:21:39For example,
00:21:41here is the number n,
00:21:43and the number n was
00:21:45divided by 3,
00:21:47and the remainder was 1.
00:21:49Here is the number n,
00:21:51divided by 4,
00:21:53how much is the remainder? 2.
00:21:55But if you see here carefully,
00:21:57the difference between 3 and 1
00:21:59is 2.
00:22:01The difference between 4 and 2 is 2.
00:22:03So the difference here
00:22:05is the same.
00:22:07The remainder was not the same,
00:22:09but the difference was the same.
00:22:11In that case,
00:22:13to find the remainder of n,
00:22:15we will directly take the LCM.
00:22:17We will take 3 and 4.
00:22:19And what will we do from that?
00:22:21We will subtract the difference here.
00:22:23This is what you have learned.
00:22:25So in yesterday's class,
00:22:27in today's class,
00:22:29we were making these two cases,
00:22:31and this was about these two cases.
00:22:33Now we will teach you the opposite.
00:22:35Now we will teach you the opposite.
00:22:37And what will we teach you here?
00:22:39Here is the number 100.
00:22:41If we divide it,
00:22:43how much is the remainder?
00:22:45The remainder is 2.
00:22:47Here is the number 100.
00:22:49If you see here,
00:22:51the greatest number which divides
00:22:53is leaving the same remainder.
00:22:55If we divide 100 by d,
00:22:57the remainder will also be 2.
00:22:59And if we divide 200 by d,
00:23:01the remainder will also be 2.
00:23:03Now here it will be said,
00:23:05do one thing,
00:23:07tell me the value of d.
00:23:09Here the divisor was given,
00:23:11but the number was missing.
00:23:13Here the number is given,
00:23:15but the divisor is missing.
00:23:17Similarly,
00:23:19what will happen in the same difference?
00:23:21In the same difference,
00:23:23it will be that the number is 100.
00:23:25If we divide it by d,
00:23:27the remainder will be 1.
00:23:29After that,
00:23:31what will happen here?
00:23:33The number is 200,
00:23:35and if we divide it by d,
00:23:37this case will not be made.
00:23:39Remove this case.
00:23:41There is no need to read this.
00:23:43There is no need to think much about this.
00:23:45We will remove this case.
00:23:47We will not read much about this case.
00:23:49We will make this case and cut it.
00:23:52We do not have to read much about this case.
00:23:55Remove this case.
00:23:57Now this case is left.
00:23:59If we have to find the divisor,
00:24:01how will we do it?
00:24:03If we have to find the divisor,
00:24:05how will we do it?
00:24:07If we divide 100 by d,
00:24:09it will be 2.
00:24:11Now in this case,
00:24:13we have to take LCM.
00:24:15And in this case,
00:24:17we have to take HCF.
00:24:19Because whenever a question is asked in this,
00:24:21it is always said
00:24:23what will be the least number?
00:24:25It is always said
00:24:27what will be the least number?
00:24:29And in this,
00:24:31if the examiner asks a question,
00:24:33he will always say
00:24:35what will be the maximum number?
00:24:37Whenever my brother speaks here,
00:24:39it will be done here
00:24:41that what will be the maximum number
00:24:43with which we divide?
00:24:45So what comes from the least,
00:24:47you can remember
00:24:49what comes from the least is LCM.
00:24:51And maximum or highest means
00:24:53HCF.
00:24:55Many children are confused
00:24:57what to take and what not to take.
00:24:59So least means to take LCM
00:25:01and maximum or highest means
00:25:03to take HCF.
00:25:05That is, if you want to solve this question,
00:25:06then in this case,
00:25:08if you want to find D,
00:25:10then what will happen to D here?
00:25:12You tell me my brother,
00:25:14you can do it in two ways here.
00:25:16One is here,
00:25:18like here,
00:25:20first you take the difference
00:25:22and take their HCF
00:25:24or first take the difference
00:25:26and then take the difference.
00:25:28My brother is equal.
00:25:30So in this case,
00:25:32what will happen here,
00:25:34understand that.
00:25:36And you, my brother,
00:25:38suppose you are dividing 8 by D,
00:25:40then how much is your remainder?
00:25:42Okay,
00:25:44is there any such number possible?
00:25:46First make an example.
00:25:48Okay,
00:25:50it is not possible here,
00:25:52like if I give you an example.
00:25:54Okay,
00:25:56you assume this,
00:25:58suppose we divide 11 by D,
00:26:00then the remainder is 1.
00:26:02And if we divide 21 by D,
00:26:04then the remainder is 1.
00:26:06It is not that
00:26:08there will be only one amount
00:26:10in the world of D,
00:26:12there can be many amounts,
00:26:14but we have to find the maximum.
00:26:16So in this case,
00:26:18what happens here,
00:26:20if we divide 21 by D,
00:26:22then the remainder is 1.
00:26:24Okay,
00:26:26if we divide 21 by D,
00:26:28then the remainder is 1.
00:26:30Okay,
00:26:32if we divide 21 by D,
00:26:34then the remainder is 1.
00:26:36Okay,
00:26:38first you see these two,
00:26:40minus this from this,
00:26:42then minus 10 from 11,
00:26:44then minus 1 from 11,
00:26:46then it will be 10.
00:26:48After that,
00:26:50minus these two,
00:26:52it will be 20.
00:26:54And what will be the answer here?
00:26:56The answer will be
00:26:58Hcf of 10, 20.
00:27:00How much will be the Hcf of these two?
00:27:02So how much will be the Hcf of these two?
00:27:04It will be 10.
00:27:06So what will be the answer for D?
00:27:08The answer will be 10.
00:27:10If you divide 11 by 10,
00:27:12then the remainder will be 1.
00:27:14If you divide 21 by 10,
00:27:16then the remainder will be 1.
00:27:18It is not necessary to divide 10 by 10,
00:27:20it can be 5 also.
00:27:22If you divide 5 by 5,
00:27:24then also 1 will come.
00:27:26It can be 2 also.
00:27:28If you divide 2 by 2,
00:27:30then also 1 will come.
00:27:32So the answer for D can be 2,
00:27:345 or 10.
00:27:36If you want to know the answer,
00:27:38then take the answer of Hcf.
00:27:40If a child does not want to do this,
00:27:42then it can be a little confusing.
00:27:44So I have a second method for him.
00:27:46He can also ask the same question in another way.
00:27:48He can say,
00:27:50how much was the answer when you divide 11 by D,
00:27:521 was coming.
00:27:54And how much was the answer when you divide 21 by D,
00:27:561 was coming.
00:27:58So when you will read Hcf later,
00:28:00the highest common factor,
00:28:02there are ways to find Hcf.
00:28:04And my brothers,
00:28:06and 21. Take their difference, what is the difference of my brother, then their difference
00:28:10is my brother is 10. So if their difference is my brother 10, then many times their difference
00:28:14or the difference of the difference is the same here hcf. hcf means highest common factor.
00:28:23That is why I said that there are many such questions of divisibility that I will not
00:28:27teach you here, which my brother I will teach you in hcf and lcm, because I have kept my
00:28:32brother in hcf. So now things will be clear by doing a little bit, rest assured. Now,
00:28:36as I told you here in this flow chart and in this flow chart, I said here that brother
00:28:41do one thing, tell me the value of this d, so first of all what you had to do, two out
00:28:46of a hundred went, so my brother 98 here and after that two out of 200 went here, so 198
00:28:52is fine. Now what to do after that, so we have to take the maximum number here, so what
00:28:57will we take here, so we will say that if you want to get the value of d, then you take
00:29:02hcf here, take the maximum number here, what to take, then take the maximum number here,
00:29:06what to take here, then take the maximum number here, so if we say here about the maximum
00:29:10number, that I have to take hcf, who has to take it, then I have to take 98 and 198.
00:29:16Now we will tell you a little concept of the maximum number, that the maximum number means
00:29:22that the maximum number that we can pick up from both places, that my brother is here,
00:29:27the maximum number is my brother here, what we do from both places, my brother, so we can
00:29:33pick it up here, okay, so if we talk about the maximum number that can be picked up from
00:29:38both places, then here it is 98, my brother is here and this is 198, if we work, then
00:29:43see, cut it, you cut it from 2 to 49 times and my brother is here, if you cut it from
00:29:502 to 9 times, then 18 and after that, what is in 9 times, okay, if we see here, then
00:29:56it will cut more, it will not cut from anyone, I have set this question a little, I feel like
00:30:06this question will not be like this, this question is wrong, we correct a little in this question,
00:30:11we add the same question in this too, we have set this question a little wrong,
00:30:16we change it here in the question, as in the question, we write the same thing,
00:30:21my brother is here to divide 31 by D, how much is our remainder, so it is coming, and how much is the
00:30:28remainder when 41 is divided by D, it is coming, so here one of the 31 will go, so our difference
00:30:33has become 30 and one of the 41 has gone, so our difference has become 40, if you want to take the
00:30:38number of D, then you will have to take hcf here, whose 30 and 40, that is, the largest number that
00:30:44will cut both and cut both, which will be my brother, which will be 10, there are many more
00:30:49questions that we will make you do back to back, so friends, when you read hcf lsim, then these
00:30:55things will be clear to us, for now you have to remember three cases, I am repeating the last time,
00:30:59after that I will not do it, concept number one, find out n and concept number two, find out d,
00:31:06n means dividend, that is, find out the share that my brother is getting here, and d means
00:31:13divisor, that is, find out about the share that is being done, okay, if we go here, then the same
00:31:20case is made, the same difference and the same remainder, so let's say the same remainder is made,
00:31:24so what do we do in hcf, we add it, what do we do in lcm, whatever remainder comes, we add it
00:31:30and the same difference is made, my brother, so the meaning of difference is to minus here,
00:31:34so what do we do in lcm, let's minus the difference, in this case you only have to read one case,
00:31:40that is, the case of the same remainder, do not do anything in this, first reduce the remainder,
00:31:45first reduce the remainder, and imagine that d will be such a number that will be either a factor of 30
00:31:50or 30, and d, see how they used to find out first, to get the value of d, they used to reduce it from here,
00:31:57in the same way, to get the value of d here, they used to reduce it from here, and said that either it
00:32:01will be 30, otherwise its factor, or it will be 40, otherwise its factor, so there will be a lot of
00:32:06factors, like 30 will be reduced from 1, 2, it will be reduced from a lot of factors,
00:32:11it will also be reduced from a lot of factors, but we will have to take a common factor of both,
00:32:15which is greater than both, like 30, either it can be 30, or it can be 1, or it can be 2, or it can be 3,
00:32:20in the same way, it will also be reduced from a lot of numbers, but my brother, we will have to take that
00:32:25number, which will also be the maximum, and will also cut both, it is 10, which can also be cut from this,
00:32:31and can also be cut from this, so what will be the answer, it will be 10.
00:32:34Now, you have understood the complete mathematics, now start asking questions from here.
00:32:41Okay, in the first one, you have to take LCM, and in the second one, you have to take HCF, remember,
00:32:46to get the value of n, you have to take LCM, to get the value of d, you have to take HCF,
00:32:51clear these things, I am not confusing, these questions are confusing themselves,
00:32:56I am making it easy, that kids, if you have to take n, you will have to take LCM,
00:33:01if you have to take d, you will have to take HCF, to get n, if the remainder is coming,
00:33:06then add it, if the difference is coming, then subtract it, and to get d, my brother, what to do here,
00:33:11so to get d, I am telling you one thing from the first day, that if you assume that the number 31
00:33:16comes when you divide by d, subtract it from this, either it will be this, or its factor,
00:33:20subtract it from this, either it will be this, or its factor, there are two conditions, so my brother,
00:33:25such a number that divides both, that is, HCF, that's it, my brother, the talk is over here,
00:33:29now here question number 28 is of the same type, we will not let the confusion come to c,
00:33:34find the largest number, from which to divide 108, 124 and 156, to get the remainder,
00:33:42find the greatest number, which divide, now see here, that number, see here,
00:33:46the greatest word is used, it means to take HCF, and which divide, which divides,
00:33:52which does not divide, which divides, so what divides is called d,
00:33:58that is, such a number, my brother, which divides 108 here, that is, the number of d is dividing it,
00:34:06then after that, here this 124, which is also divided by d, and 156, which is also divided by d,
00:34:12so such a number, my brother, which divides it by d, which divides it by d, which divides it by d,
00:34:18and at every place, they give the same remainder, my brother, how much they give here,
00:34:22then give r, now in this case, my brother, what is here, then there is no information about the remainder,
00:34:28my brother, there is no information about the remainder, how much will be the remainder,
00:34:32so I want to tell you the same thing here, understand, here first of all you have to understand one thing,
00:34:38and that my brother is here, h, c and f, highest common factor, what is this HCF, my brother,
00:34:46and how do we get it, okay, so first we give you a little information about HCF,
00:34:52and after that it will be easy for you to ask questions, my brother, highest common factor here,
00:34:58now suppose I have written two numbers here, one 12 is written and one 18 is written,
00:35:02so what will be their HCF here, now the first thing you will see here is that the word factor is involved,
00:35:08okay, so the number from which 12 is deducted, it will be deducted from 1, 2, 3,
00:35:14after that it will be deducted from 6, and after that, my brother, it will be deducted from 12 here,
00:35:18okay, from 3, my brother, it will be deducted from 4 here, so it will be 3, then after that it will be 4,
00:35:24then it will be 6, and then how much will be 12, let's talk about 18, it will be deducted from 1,
00:35:30it will be deducted from 2, it will be deducted from 3, it will be deducted from 6, it will be deducted from 9,
00:35:34it will be deducted from 10, it will be deducted from 11, it will be deducted from 12, and it will be deducted from 18,
00:35:38now there are many such common factors in them, what is the meaning of common factor,
00:35:42which is common in both, you will see, sir, 1 and 1 are also common, 2 and 2 are also common,
00:35:463 and 3 are also common, 6 and 6 are also common, but when it comes to highest common factor,
00:35:52then the common factor which is the largest, then this is my brother, HCF is here, okay,
00:35:58if we subtract two numbers here, my brother, 12 and 18, we subtract HCF,
00:36:02so how much does the 12-18 HCF come out, it comes out 6,
00:36:06that is, the largest number that comes out of both,
00:36:10so how much will be the largest number, it will be 6, which will be common in both,
00:36:14okay, this is its definition, whose definition is it, it is the definition of HCF,
00:36:18now there are two ways to subtract HCF,
00:36:22okay, and why are they two ways, like here,
00:36:26my brother, the concept of small numbers is different,
00:36:30for small numbers here, if we talk in simple language,
00:36:34okay, and my brother, for large numbers, it is different,
00:36:38and I have made it myself, that if you want to subtract a small number,
00:36:42then subtract it from a different method, and if you want to subtract a large number,
00:36:46then subtract it from a different method, it will be very beneficial for me,
00:36:50like, let's say it is a small number, and what is the small number here,
00:36:54it is 26, this is a small number, what do you do here,
00:36:58then my brother, subtract HCF, so do them with prime factorization,
00:37:02prime factorization means here, like 14, or a little more,
00:37:06my brother, let's take some big numbers, like let's say we took 20 here,
00:37:10and after that, my brother, we took 20 here,
00:37:14and how much did we take here, my brother, let's take 76,
00:37:18so what are we taking for 20 and 76, let's take HCF,
00:37:22HCF is a common factor, so what do we do here,
00:37:26let's do it with prime factorization, first, we will divide by the smallest number,
00:37:30which will cut both, so if you divide by 2, then in 10 times,
00:37:34and if you divide by 2, then in 3 times, and in 8 times, and my brother,
00:37:38if you divide by 2, then in 5 times, and if you divide by 2, then in 19 times,
00:37:42so what will be your HCF here, my brother,
00:37:46so what does a person do while taking HCF,
00:37:50my brother, he does not take the lower part,
00:37:54he does not take the lower part, and this is the condition of HCF,
00:37:58that whatever number you take, it should cut everyone,
00:38:02my brother, the condition of HCF is that whatever you take, it should cut everyone,
00:38:06so what will be the HCF here, my brother, it will be 4,
00:38:10what will be the HCF, it will be 4, but if you take some big numbers,
00:38:14like big numbers, let's say you have 2001 here,
00:38:18similarly, my brother, you have 5001 here,
00:38:22and what has come here, so let's say my brother, you have 7002 here,
00:38:26and in this case, some big numbers here,
00:38:30in a way, which my brother, we have to take HCF here,
00:38:34the highest common factor, that we can take the biggest common here,
00:38:38so what is the meaning of taking the biggest common here,
00:38:42so if you want to take the biggest common, then you do not have to adopt this method,
00:38:46what you have to adopt is, take the difference of these,
00:38:50so when you take the difference of these, what will be the difference of these,
00:38:52it will be 3000, my brother,
00:38:54after that, you take the difference of these,
00:38:56what will be the difference of these,
00:38:58so the difference of these, my brother, will be of 1001,
00:39:02not 1001, it means,
00:39:04okay,
00:39:06we are going to get the difference of 2001,
00:39:08here we are going to get 2001,
00:39:10okay, 5000, 2000, 7000, 2001,
00:39:14and if we see the difference of these,
00:39:16what will be the difference of these,
00:39:18it will be 999,
00:39:20it is going to be 999,
00:39:22okay, so it is going to be 999,
00:39:24now, let me give you another example,
00:39:28let me give you another example,
00:39:30this will also fit us,
00:39:34but this is not 999,
00:39:36it means,
00:39:38let us not consider this example too much,
00:39:40let us consider another example,
00:39:42okay,
00:39:44in which you will get a little benefit,
00:39:46let us say,
00:39:48let us take 51 here,
00:39:50okay,
00:39:52let us not take 51,
00:39:54let us take the same number,
00:39:56108, 124, 156,
00:39:58let us take the same number of these people,
00:40:00which is given in the question,
00:40:02here 108, 124, 156,
00:40:04let us take the same number of these people,
00:40:06so let us say, it is 108,
00:40:08after that it is 124,
00:40:10after that it is 156,
00:40:12now this is 108, 124, 156,
00:40:14when you will take it from this method,
00:40:16it will take you a lot of time,
00:40:18you can calculate it once,
00:40:20let me show you the calculation here,
00:40:22this is 108,
00:40:24after that this is 124,
00:40:26and this is 156,
00:40:28if I have to find the biggest number,
00:40:30which will divide all three,
00:40:32so how to do it,
00:40:34first we will divide it by 2,
00:40:36how many times, in 54 times,
00:40:38and in 2 to 78 times,
00:40:40and how to divide it,
00:40:42in 2 times,
00:40:44and in 7 times,
00:40:46and in 31 times,
00:40:48and in 3 times,
00:40:50and in 9 times,
00:40:52is there any number here,
00:40:54which can divide all of them,
00:40:56you will say no,
00:40:58there is no such number left,
00:41:00which can divide all of them,
00:41:02so if we talk about HCF,
00:41:04so what is 2 into 2,
00:41:06so this is 4,
00:41:08so what is 4 here,
00:41:10so similarly,
00:41:12if there is a big number here,
00:41:14so this is the method,
00:41:16108, 124, 156,
00:41:18divided by 2 in 24 times,
00:41:20in 62 times, and in 78 times,
00:41:22divided by 2 in 27 times,
00:41:24in 31 times, and in 39 times,
00:41:26but I will say don't do like that,
00:41:28you apply the difference method,
00:41:30take their difference here,
00:41:32so what is the difference of these two,
00:41:34take their difference here,
00:41:36so what is the difference of these two,
00:41:38so you will say 32,
00:41:40take their difference here,
00:41:42so what is the difference of these two,
00:41:44it will be 16,
00:41:46now either this person can answer himself,
00:41:48or some factor of this can answer,
00:41:50so divide this by 16,
00:41:52so if 16 is dividing this,
00:41:54so you will say no,
00:41:5616 is not dividing this,
00:41:58so it means 16 will not answer,
00:42:00then what is the factor of 16,
00:42:02then what is the factor of 16,
00:42:04then what is the factor of 16,
00:42:06then what is the factor of 16,
00:42:08then what is the factor of 16,
00:42:10then what is the factor of 16,
00:42:12then what is the factor of 16,
00:42:14then what is the factor of 16,
00:42:16then what is the factor of 16,
00:42:18then what is the factor of 16,
00:42:20then what is the factor of 16,
00:42:22then what is the factor of 16,
00:42:24then what is the factor of 16,
00:42:26then what is the factor of 16,
00:42:28then what is the factor of 16,
00:42:30then what is the factor of 16,
00:42:32then what is the factor of 16,
00:42:34then what is the factor of 16,
00:42:36then what is the factor of 16,
00:42:38then what is the factor of 16,
00:42:40then what is the factor of 16,
00:42:42then what is the factor of 16,
00:42:44then what is the factor of 16,
00:42:46then what is the factor of 16,
00:42:48then what is the factor of 16,
00:42:50then what is the factor of 16,
00:42:52then what is the factor of 16,
00:42:54then what is the factor of 16,
00:42:56then what is the factor of 16,
00:42:58then what is the factor of 16,
00:43:00then what is the factor of 16,
00:43:02then what is the factor of 16,
00:43:04then what is the factor of 16,
00:43:06then what is the factor of 16,
00:43:08then what is the factor of 16,
00:43:10then what is the factor of 16,
00:43:12then what is the factor of 16,
00:43:14then what is the factor of 16,
00:43:16then what is the factor of 16,
00:43:18then what is the factor of 16,
00:43:20then what is the factor of 16,
00:43:22then what is the factor of 16,
00:43:24then what is the factor of 16,
00:43:26then what is the factor of 16,
00:43:28then what is the factor of 16,
00:43:30then what is the factor of 16,
00:43:32then what is the factor of 16,
00:43:34then what is the factor of 16,
00:43:36then what is the factor of 16,
00:43:38then what is the factor of 16,
00:43:40then what is the factor of 16,
00:43:42then what is the factor of 16,
00:43:44then what is the factor of 16,
00:43:46then what is the factor of 16,
00:43:48then what is the factor of 16,
00:43:50then what is the factor of 16,
00:43:52then what is the factor of 16,
00:43:54then what is the factor of 16,
00:43:56then what is the factor of 16,
00:43:58then what is the factor of 16,
00:44:00then what is the factor of 16,
00:44:02then what is the factor of 16,
00:44:04then what is the factor of 16,
00:44:06then what is the factor of 16,
00:44:08then what is the factor of 16,
00:44:10then what is the factor of 16,
00:44:12then what is the factor of 16,
00:44:14then what is the factor of 16,
00:44:16then what is the factor of 16,
00:44:18then what is the factor of 16,
00:44:20then what is the factor of 16,
00:44:22then what is the factor of 16,
00:44:24then what is the factor of 16,
00:44:26then what is the factor of 16,
00:44:28then what is the factor of 16,
00:44:30then what is the factor of 16,
00:44:32then what is the factor of 16,
00:44:34then what is the factor of 16,
00:44:36then what is the factor of 16,
00:44:38then what is the factor of 16,
00:44:40then what is the factor of 16,
00:44:42then what is the factor of 16,
00:44:44then what is the factor of 16,
00:44:46then what is the factor of 16,
00:44:48then what is the factor of 16,
00:44:50then what is the factor of 16,
00:44:52then what is the factor of 16,
00:44:54then what is the factor of 16,
00:44:56then what is the factor of 16,
00:44:58then what is the factor of 16,
00:45:00then what is the factor of 16,
00:45:02then what is the factor of 16,
00:45:04then what is the factor of 16,
00:45:06then what is the factor of 16,
00:45:08then what is the factor of 16,
00:45:10then what is the factor of 16,
00:45:12then what is the factor of 16,
00:45:14then what is the factor of 16,
00:45:16then what is the factor of 16,
00:45:18then what is the factor of 16,
00:45:20then what is the factor of 16,
00:45:22then what is the factor of 16,
00:45:24then what is the factor of 16,
00:45:26then what is the factor of 16,
00:45:28then what is the factor of 16,
00:45:30then what is the factor of 16,
00:45:32then what is the factor of 16,
00:45:34then what is the factor of 16,
00:45:36then what is the factor of 16,
00:45:38then what is the factor of 16,
00:45:40then what is the factor of 16,
00:45:42then what is the factor of 16,
00:45:44then what is the factor of 16,
00:45:46then what is the factor of 16,
00:45:48then what is the factor of 16,
00:45:50then what is the factor of 16,
00:45:52then what is the factor of 16,
00:45:54then what is the factor of 16,
00:45:56then what is the factor of 16,
00:45:58then what is the factor of 16,
00:46:00then what is the factor of 16,
00:46:02then what is the factor of 16,
00:46:04then what is the factor of 16,
00:46:06then what is the factor of 16,
00:46:08then what is the factor of 16,
00:46:10then what is the factor of 16,
00:46:12then what is the factor of 16,
00:46:14then what is the factor of 16,
00:46:16then what is the factor of 16,
00:46:18then what is the factor of 16,
00:46:20then what is the factor of 16,
00:46:22then what is the factor of 16,
00:46:24then what is the factor of 16,
00:46:26then what is the factor of 16,
00:46:28then what is the factor of 16,
00:46:30then what is the factor of 16,
00:46:32then what is the factor of 16,
00:46:34then what is the factor of 16,
00:46:36then what is the factor of 16,
00:46:38then what is the factor of 16,
00:46:40then what is the factor of 16,
00:46:42then what is the factor of 16,
00:46:44then what is the factor of 16,
00:46:46then what is the factor of 16,
00:46:48then what is the factor of 16,
00:46:50then what is the factor of 16,
00:46:52then what is the factor of 16,
00:46:54then what is the factor of 16,
00:46:56then what is the factor of 16,
00:46:58then what is the factor of 16,
00:47:00then what is the factor of 16,
00:47:02then what is the factor of 16,
00:47:04then what is the factor of 16,
00:47:06then what is the factor of 16,
00:47:08then what is the factor of 16,
00:47:10then what is the factor of 16,
00:47:12then what is the factor of 16,
00:47:14then what is the factor of 16,
00:47:16then what is the factor of 16,
00:47:18then what is the factor of 16,
00:47:20then what is the factor of 16,
00:47:22then what is the factor of 16,
00:47:24then what is the factor of 16,
00:47:26then what is the factor of 16,
00:47:28then what is the factor of 16,
00:47:30then what is the factor of 16,
00:47:32then what is the factor of 16,
00:47:34then what is the factor of 16,
00:47:36then what is the factor of 16,
00:47:38now here the remainder is given,
00:47:40this is our work is easy,
00:47:42what is the greatest number by which this,
00:47:44this and this are divided and
00:47:46remainder is 6 in each case,
00:47:48here they have given the remainder,
00:47:50so here they have given the remainder,
00:47:52so it is a good thing,
00:47:54so we will say sir it is 156,
00:47:56we have to divide it from D,
00:47:58and how much is the remainder,
00:48:00it is 6,
00:48:02after that it is 181,
00:48:04we have to divide it from D,
00:48:06after that it is 181,
00:48:08we have to divide it from D,
00:48:10and how much is the remainder,
00:48:12it is 6,
00:48:14so I forgot one thing here,
00:48:16first you minus it from this,
00:48:18how much will come,
00:48:20150,
00:48:22after that you minus it from this,
00:48:24you will get 175,
00:48:26after that you minus it from this,
00:48:28you will get 325,
00:48:30after that if you want to subtract D,
00:48:32see what is the way to subtract D,
00:48:34see what is the way to subtract D,
00:48:36see what is the way to subtract D,
00:48:38see what is the way to subtract D,
00:48:40see what is the way to subtract D,
00:48:42see what is the way to subtract D,
00:48:44see what is the way to subtract D,
00:48:46see what is the way to subtract D,
00:48:48see what is the way to subtract D,
00:48:50see what is the way to subtract D,
00:48:52see what is the way to subtract D,
00:48:54see what is the way to subtract D,
00:48:56see what is the way to subtract D,
00:48:58see what is the way to subtract D,
00:49:00see what is the way to subtract D,
00:49:02see what is the way to subtract D,
00:49:04see what is the way to subtract D,
00:49:06see what is the way to subtract D,
00:49:08see what is the way to subtract D,
00:49:10see what is the way to subtract D,
00:49:12see what is the way to subtract D,
00:49:14see what is the way to subtract D,
00:49:16see what is the way to subtract D,
00:49:18see what is the way to subtract D,
00:49:20see what is the way to subtract D,
00:49:22see what is the way to subtract D,
00:49:24see what is the way to subtract D,
00:49:26see what is the way to subtract D,
00:49:28see what is the way to subtract D,
00:49:30see what is the way to subtract D,
00:49:32see what is the way to subtract D,
00:49:34see what is the way to subtract D,
00:49:36see what is the way to subtract D,
00:49:38see what is the way to subtract D,
00:49:40see what is the way to subtract D,
00:49:42see what is the way to subtract D,
00:49:44see what is the way to subtract D,
00:49:46see what is the way to subtract D,
00:49:48see what is the way to subtract D,
00:49:50see what is the way to subtract D,
00:49:52see what is the way to subtract D,
00:49:54see what is the way to subtract D,
00:49:56see what is the way to subtract D,
00:49:58see what is the way to subtract D,
00:50:00see what is the way to subtract D,
00:50:02see what is the way to subtract D,
00:50:04see what is the way to subtract D,
00:50:06see what is the way to subtract D,
00:50:08see what is the way to subtract D,
00:50:10see what is the way to subtract D,
00:50:12see what is the way to subtract D,
00:50:14see what is the way to subtract D,
00:50:16see what is the way to subtract D,
00:50:18see what is the way to subtract D,
00:50:20see what is the way to subtract D,
00:50:22see what is the way to subtract D,
00:50:24see what is the way to subtract D,
00:50:26see what is the way to subtract D,
00:50:28see what is the way to subtract D,
00:50:30see what is the way to subtract D,
00:50:32see what is the way to subtract D,
00:50:34see what is the way to subtract D,
00:50:36see what is the way to subtract D,
00:50:38see what is the way to subtract D,
00:50:40see what is the way to subtract D,
00:50:42see what is the way to subtract D,
00:50:44see what is the way to subtract D,
00:50:46see what is the way to subtract D,
00:50:48see what is the way to subtract D,
00:50:50see what is the way to subtract D,
00:50:52see what is the way to subtract D,
00:50:54see what is the way to subtract D,
00:50:56see what is the way to subtract D,
00:50:58see what is the way to subtract D,
00:51:00see what is the way to subtract D,
00:51:02see what is the way to subtract D,
00:51:04see what is the way to subtract D,
00:51:06see what is the way to subtract D,
00:51:08see what is the way to subtract D,
00:51:10see what is the way to subtract D,
00:51:12see what is the way to subtract D,
00:51:14see what is the way to subtract D,
00:51:16see what is the way to subtract D,
00:51:18see what is the way to subtract D,
00:51:20see what is the way to subtract D,
00:51:22see what is the way to subtract D,
00:51:24see what is the way to subtract D,
00:51:26see what is the way to subtract D,
00:51:28see what is the way to subtract D,
00:51:30see what is the way to subtract D,
00:51:32see what is the way to subtract D,
00:51:34see what is the way to subtract D,
00:51:36see what is the way to subtract D,
00:51:38see what is the way to subtract D,
00:51:40see what is the way to subtract D,
00:51:42see what is the way to subtract D,
00:51:44see what is the way to subtract D,
00:51:46see what is the way to subtract D,
00:51:48see what is the way to subtract D,
00:51:50see what is the way to subtract D,
00:51:52see what is the way to subtract D,
00:51:54see what is the way to subtract D,
00:51:56see what is the way to subtract D,
00:51:58see what is the way to subtract D,
00:52:00see what is the way to subtract D,
00:52:02see what is the way to subtract D,
00:52:04see what is the way to subtract D,
00:52:06see what is the way to subtract D,
00:52:08see what is the way to subtract D,
00:52:10see what is the way to subtract D,
00:52:12see what is the way to subtract D,
00:52:14see what is the way to subtract D,
00:52:16see what is the way to subtract D,
00:52:18see what is the way to subtract D,
00:52:20see what is the way to subtract D,
00:52:22see what is the way to subtract D,
00:52:24see what is the way to subtract D,
00:52:26see what is the way to subtract D,
00:52:28see what is the way to subtract D,
00:52:30see what is the way to subtract D,
00:52:32see what is the way to subtract D,
00:52:34see what is the way to subtract D,
00:52:36see what is the way to subtract D,
00:52:38see what is the way to subtract D,
00:52:40see what is the way to subtract D,
00:52:42see what is the way to subtract D,
00:52:44see what is the way to subtract D,
00:52:46see what is the way to subtract D,
00:52:48see what is the way to subtract D,
00:52:50see what is the way to subtract D,
00:52:52see what is the way to subtract D,
00:52:54see what is the way to subtract D,
00:52:56see what is the way to subtract D,
00:52:58see what is the way to subtract D,
00:53:00see what is the way to subtract D,
00:53:02see what is the way to subtract D,
00:53:04see what is the way to subtract D,
00:53:06see what is the way to subtract D,
00:53:08see what is the way to subtract D,
00:53:10see what is the way to subtract D,
00:53:12see what is the way to subtract D,
00:53:14see what is the way to subtract D,
00:53:16see what is the way to subtract D,
00:53:18see what is the way to subtract D,
00:53:20see what is the way to subtract D,
00:53:22see what is the way to subtract D,
00:53:24see what is the way to subtract D,
00:53:26see what is the way to subtract D,
00:53:28see what is the way to subtract D,
00:53:30see what is the way to subtract D,
00:53:32see what is the way to subtract D,
00:53:34see what is the way to subtract D,
00:53:36see what is the way to subtract D,
00:53:38see what is the way to subtract D,
00:53:40see what is the way to subtract D,
00:53:42see what is the way to subtract D,
00:53:44see what is the way to subtract D,
00:53:46see what is the way to subtract D,
00:53:48see what is the way to subtract D,
00:53:50see what is the way to subtract D,
00:53:52see what is the way to subtract D,
00:53:54see what is the way to subtract D,
00:53:56see what is the way to subtract D,
00:53:58see what is the way to subtract D,
00:54:00see what is the way to subtract D,
00:54:02see what is the way to subtract D,
00:54:04see what is the way to subtract D,
00:54:06see what is the way to subtract D,
00:54:08see what is the way to subtract D,
00:54:10see what is the way to subtract D,
00:54:12see what is the way to subtract D,
00:54:14see what is the way to subtract D,
00:54:16see what is the way to subtract D,
00:54:18see what is the way to subtract D,
00:54:20see what is the way to subtract D,
00:54:22see what is the way to subtract D,
00:54:24see what is the way to subtract D,
00:54:26see what is the way to subtract D,
00:54:28see what is the way to subtract D,
00:54:30see what is the way to subtract D,
00:54:32see what is the way to subtract D,
00:54:34see what is the way to subtract D,
00:54:36see what is the way to subtract D,
00:54:38see what is the way to subtract D,
00:54:40see what is the way to subtract D,
00:54:42see what is the way to subtract D,
00:54:44see what is the way to subtract D,
00:54:46see what is the way to subtract D,
00:54:48see what is the way to subtract D,
00:54:50see what is the way to subtract D,
00:54:52see what is the way to subtract D,
00:54:54see what is the way to subtract D,
00:54:56see what is the way to subtract D,
00:54:58see what is the way to subtract D,
00:55:00see what is the way to subtract D,
00:55:02see what is the way to subtract D,
00:55:04see what is the way to subtract D,
00:55:06see what is the way to subtract D,
00:55:08see what is the way to subtract D,
00:55:10see what is the way to subtract D,
00:55:12see what is the way to subtract D,
00:55:14see what is the way to subtract D,
00:55:16see what is the way to subtract D,
00:55:18see what is the way to subtract D,
00:55:20see what is the way to subtract D,
00:55:22see what is the way to subtract D,
00:55:24see what is the way to subtract D,
00:55:26see what is the way to subtract D,
00:55:28see what is the way to subtract D,
00:55:30see what is the way to subtract D,
00:55:32see what is the way to subtract D,
00:55:34see what is the way to subtract D,
00:55:36see what is the way to subtract D,
00:55:38see what is the way to subtract D,
00:55:40see what is the way to subtract D,
00:55:42see what is the way to subtract D,
00:55:44see what is the way to subtract D,
00:55:46see what is the way to subtract D,
00:55:48see what is the way to subtract D,
00:55:50see what is the way to subtract D,
00:55:52see what is the way to subtract D,
00:55:54see what is the way to subtract D,
00:55:56see what is the way to subtract D,
00:55:58see what is the way to subtract D,
00:56:00see what is the way to subtract D,
00:56:02see what is the way to subtract D,
00:56:04see what is the way to subtract D,
00:56:06see what is the way to subtract D,
00:56:08see what is the way to subtract D,
00:56:10see what is the way to subtract D,
00:56:12see what is the way to subtract D,
00:56:14see what is the way to subtract D,
00:56:16see what is the way to subtract D,
00:56:18see what is the way to subtract D,
00:56:20see what is the way to subtract D,
00:56:22see what is the way to subtract D,
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00:56:30see what is the way to subtract D,
00:56:32see what is the way to subtract D,
00:56:34see what is the way to subtract D,
00:56:36see what is the way to subtract D,
00:56:38see what is the way to subtract D,
00:56:40see what is the way to subtract D,
00:56:42see what is the way to subtract D,
00:56:44see what is the way to subtract D,
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00:56:48see what is the way to subtract D,
00:56:50see what is the way to subtract D,
00:56:52see what is the way to subtract D,
00:56:54see what is the way to subtract D,
00:56:56see what is the way to subtract D,
00:56:58see what is the way to subtract D,
00:57:00see what is the way to subtract D,
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00:57:08see what is the way to subtract D,
00:57:10see what is the way to subtract D,
00:57:12see what is the way to subtract D,
00:57:14see what is the way to subtract D,
00:57:16see what is the way to subtract D,
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00:57:20see what is the way to subtract D,
00:57:22see what is the way to subtract D,
00:57:24see what is the way to subtract D,
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00:58:00see what is the way to subtract D,
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01:00:00see what is the way to subtract D,
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01:00:04see what is the way to subtract D,
01:00:06see what is the way to subtract D,
01:00:08see what is the way to subtract D,
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01:00:14see what is the way to subtract D,
01:00:16see what is the way to subtract D,
01:00:18see what is the way to subtract D,
01:00:20see what is the way to subtract D,
01:00:22see what is the way to subtract D,
01:00:24see what is the way to subtract D,
01:00:26see what is the way to subtract D,
01:00:28see what is the way to subtract D,
01:00:30see what is the way to subtract D,
01:00:32see what is the way to subtract D,
01:00:34see what is the way to subtract D,
01:00:36see what is the way to subtract D,
01:00:38see what is the way to subtract D,
01:00:40see what is the way to subtract D,
01:00:42see what is the way to subtract D,
01:00:44see what is the way to subtract D,
01:00:46see what is the way to subtract D,
01:00:48see what is the way to subtract D,
01:00:50see what is the way to subtract D,
01:00:52see what is the way to subtract D,
01:00:54see what is the way to subtract D,
01:00:56see what is the way to subtract D,
01:00:58see what is the way to subtract D,
01:01:00see what is the way to subtract D,
01:01:02see what is the way to subtract D,
01:01:04see what is the way to subtract D,
01:01:06see what is the way to subtract D,
01:01:08see what is the way to subtract D,
01:01:10see what is the way to subtract D,
01:01:12see what is the way to subtract D,
01:01:14see what is the way to subtract D,
01:01:16see what is the way to subtract D,
01:01:18see what is the way to subtract D,
01:01:20see what is the way to subtract D,
01:01:22see what is the way to subtract D,
01:01:24see what is the way to subtract D,
01:01:26see what is the way to subtract D,
01:01:28see what is the way to subtract D,
01:01:30see what is the way to subtract D,
01:01:32see what is the way to subtract D,
01:01:34see what is the way to subtract D,
01:01:36see what is the way to subtract D,
01:01:38see what is the way to subtract D,
01:01:40see what is the way to subtract D,
01:01:42see what is the way to subtract D,
01:01:44see what is the way to subtract D,
01:01:46see what is the way to subtract D,
01:01:48see what is the way to subtract D,
01:01:50see what is the way to subtract D,
01:01:52see what is the way to subtract D,
01:01:54see what is the way to subtract D,
01:01:56see what is the way to subtract D,
01:01:58see what is the way to subtract D,
01:02:00see what is the way to subtract D,
01:02:02see what is the way to subtract D,
01:02:04see what is the way to subtract D,
01:02:06see what is the way to subtract D,
01:02:08see what is the way to subtract D,
01:02:10see what is the way to subtract D,
01:02:12see what is the way to subtract D,
01:02:14see what is the way to subtract D,
01:02:16see what is the way to subtract D,
01:02:18see what is the way to subtract D,
01:02:20see what is the way to subtract D,
01:02:22see what is the way to subtract D,
01:02:24see what is the way to subtract D,
01:02:26see what is the way to subtract D,
01:02:28see what is the way to subtract D,
01:02:30see what is the way to subtract D,
01:02:32see what is the way to subtract D,
01:02:34see what is the way to subtract D,
01:02:36see what is the way to subtract D,
01:02:38see what is the way to subtract D,
01:02:40see what is the way to subtract D,
01:02:42see what is the way to subtract D,
01:02:44see what is the way to subtract D,
01:02:46see what is the way to subtract D,
01:02:48see what is the way to subtract D,
01:02:50see what is the way to subtract D,
01:02:52see what is the way to subtract D,
01:02:54see what is the way to subtract D,
01:02:56see what is the way to subtract D,
01:02:58see what is the way to subtract D,
01:03:00see what is the way to subtract D,