Number System 27
Transcript
00:00:00Today is the last class of your remainder and after this class, your remainder will end and after that, we will start a new topic in the next class.
00:00:29How are you all? Good evening, good evening, good evening to everyone.
00:00:36There is no voice. There is a voice. Tell me properly. Sir, check the voice once.
00:00:50Hello, hello, hello. There is a voice. You are getting worried.
00:00:55Sir, there is a voice. Very good, very good. How are you feeling after reading the remainder? Are you enjoying it?
00:01:03Tell me, are you enjoying it or not?
00:01:07You are enjoying it. Very good.
00:01:09So today we are going to teach you a special concept and through this special concept, we will teach you a lot of things.
00:01:15But before that, we had done question number 58. First, we will do question number 59 and the rest of the questions.
00:01:22And the questions that we have left behind, we will do them once and understand them too.
00:01:28So let's see question number 59. What was said? Read it.
00:01:33If we talk about this question, then it is said in the question that if we divide the remainder by 15, then what will happen?
00:01:45So we said here, understand what I am saying. Here it is 1 factorial and after that it is 2 factorial and after that it is 3 factorial and after that it is 4 factorial.
00:02:04And by doing this, this story will go up to 120 factorial.
00:02:10And whom do we have to divide this? We have to divide this by 15.
00:02:15That means you divide this by 15, divide this by 15, divide this by 15, divide this by 15 and when you have 5 factorial here, then you have to divide 5 factorial by 15.
00:02:286 factorial will come, you have to do that too. 7 factorial will come, you have to do that too.
00:02:34And you have to divide each number here and tell the answer.
00:02:40Now a small thing here, you will have to understand one thing and I will write it a little on the side.
00:02:47When we write 1 factorial, then what does 1 factorial mean? It is 1.
00:02:51When we write 2 factorial, then what does 2 into mean? 1 means 2.
00:02:55When we write 3 factorial, then it means 3 into 2 into 1 means 6.
00:03:02When we write 4 factorial, it means 4 to 1 is multiplied continuously and this value is 24.
00:03:10When we write 5 factorial, then 5 to 5 means 5 into 4 into 3 into 2 into 1 means 120.
00:03:19What do we do with all these things here? We multiply.
00:03:23If we look here, then what will we say here? We will say 1 factorial.
00:03:281 factorial means 1 and we will divide 1 by 15.
00:03:332 factorial, 2 factorial means 2 and here 2 will be divided by 15.
00:03:39After that, 3 factorial, 3 factorial means 6 and this 6 will be divided by 15.
00:03:454 factorial, whose value is 24 and we will divide it by 15.
00:03:51After that, when you write 5 factorial, then 5 factorial means 5 into 4 into 3 into 2 into 1.
00:04:02When we divide it by 15, then what will happen here? It will become completely divisible.
00:04:08And it will become divisible like 5 and 3 will completely divide 15.
00:04:12And if this number will divide the above, then what will we get in the name of remainder? We will get 0.
00:04:18It means that some remainder will be obtained from this.
00:04:21What I mean to say is that if you divide 1 by 15, then remainder 1 will come.
00:04:25If you divide 2 by 15, then remainder 2 will come.
00:04:28If you divide 6 by 15, then this much will come.
00:04:30If you divide 24 by 15, then 1 times 15 is 15.
00:04:33If 9 is left, then 9 will come here.
00:04:34But after this, it is like 5 factorial.
00:04:38So, in 5 factorial, 5 and 3 both come.
00:04:42If 5 and 3 both come, then it will divide 15.
00:04:44In 6 factorial, 5 and 3 both will come, which will divide 15.
00:04:48In 7 factorial, 5 and 3 both will come, which will divide 15.
00:04:52So, after 5 factorial, how much remainder is going to come in all the numbers?
00:04:57So, my brother 0, then after that 0, then after that 0, then after that 0 and so on.
00:05:04If we see, then we will say 9, 6, 15, 2, 17, and 1, 18, 18 is coming.
00:05:09From whom should we divide 18 again?
00:05:11Why from 15?
00:05:13Because this is bigger than the one below.
00:05:16This is bigger than our divisor.
00:05:18And when we divide again, then how much will come?
00:05:203 will come.
00:05:22So, the correct answer will be option number D.
00:05:24You can understand this question in a very easy language.
00:05:26And how can you do it in a very easy language?
00:05:29So, my brother, I have written like this to write here.
00:05:31So, my brother, you can understand this in such a short cut.
00:05:34See, Guruji, leave all these stories.
00:05:36You don't have to write so much here and tell and work so hard.
00:05:40We understand one thing in a better way.
00:05:43And what do we understand here?
00:05:45We see this thing here.
00:05:47Sir, see, understand a small thing here.
00:05:49All these are factorial.
00:05:51If we divide here from 15, then from whom do we divide?
00:05:55From 15.
00:05:57So, you know, from 15, the value of 1 factorial is 1.
00:05:59The value of 2 factorial is 2.
00:06:01The value of 3 factorial is 6.
00:06:03The value of 4 factorial is 24.
00:06:05And after that, 5 into 3 will come here, which will give the remainder 0.
00:06:095 into 3 will come, which will give the remainder.
00:06:11Now, if you see after that, then here 24 and 6, which is 30, my brother,
00:06:1630 will be completely cut from 15.
00:06:18And if it is cut, then how much will be left?
00:06:203 will be the answer.
00:06:22Option number D is the correct answer here.
00:06:26Shivam says, I have been commenting for a long time.
00:06:29Please read it today.
00:06:31Please, Prem Anand Ji Maharaj is remembering.
00:06:33What are you saying, brother?
00:06:35What do you want to say, Shivam Sharma?
00:06:37Tell me here.
00:06:39So, you understood what I was saying.
00:06:41So, what we wanted to say here, we wanted to say here.
00:06:43The value of this factorial is this much, the value of this is this much, the value of this is this much, the value of this is this much.
00:06:47And after here, at every place, 5 and 3 will come continuously.
00:06:52Will keep coming, will keep coming, will keep coming.
00:06:53And after that, this will also be cut from 15.
00:06:556 factorial will be cut, 7 factorial will be cut.
00:06:57So, the next one, whether it is up to 120 factorial, or up to 200 factorial, or up to 500, or up to 1000, it does not matter.
00:07:05Because all my brothers will be cut from 15.
00:07:07Now here the remainder is 24, here the remainder is 6.
00:07:09So, 24 and 6 is 30.
00:07:11It will be cut from 15 again.
00:07:13Do you understand?
00:07:15My brother will be cut from 15 again.
00:07:17Some people think that the value of 5 factorial is 0.
00:07:19It is not 0.
00:07:21The value of 5 factorial is 120.
00:07:23If you divide 120 by 15, the remainder will be 0.
00:07:25Ok.
00:07:27You talk like a fool.
00:07:29You talk like a fool.
00:07:31Now see here.
00:07:33This is the value of 5 factorial, which is 120.
00:07:35If you divide 120 by 15, then 15 times 8 is equal to 120.
00:07:40So, the remainder will not be 0.
00:07:42It will not be 0.
00:07:44So, if you divide 5 factorial by 15, it will be 0.
00:07:46Then 0, then 0.
00:07:48So, 0 will keep coming here.
00:07:50Ok.
00:07:51Do you understand what I am saying?
00:07:53Ok.
00:07:55Let me give you a question.
00:07:57Look at the question here.
00:07:59Suppose we told you 1 factorial.
00:08:01Then we told you 2 factorial.
00:08:03Then we told you 3 factorial.
00:08:05Then we told you 4 factorial.
00:08:07Ok.
00:08:09And after that, my brother will be 5 factorial.
00:08:11And in that way, let's assume that we have gone up to 1000 factorial.
00:08:15I said that if you divide all these people by 5, then tell me the remainder.
00:08:19Now what will you say here?
00:08:21So, Guruji will say, look,
00:08:23what is the value of 1 factorial here?
00:08:252 factorial means 2.
00:08:273 factorial means 3 into 2 is 6.
00:08:294 factorial means 4, 3, 12, 2, 24.
00:08:32And as you write 5 factorial,
00:08:345 comes inside this.
00:08:36What comes inside this? 5 comes.
00:08:38What is the meaning of 5 factorial?
00:08:405 into 4 into 3 into 2 into 1, my brother.
00:08:43Ok.
00:08:45After that, as you write 6 factorial,
00:08:476 factorial means 6 into 5 into 4 into 3 into 2 into 1.
00:08:51Assume that this will come here.
00:08:53And how far will this sequence go?
00:08:55Assume that this sequence will go up to 1000 factorial.
00:08:58Divide this by 5 here.
00:09:00Divide this by 5 here.
00:09:02Divide this by 5 here, my brother.
00:09:04Divide this by 5 here.
00:09:06Divide this by 5 here.
00:09:08Now tell me one thing here.
00:09:10If you divide 1 by 5, the remainder will be 1.
00:09:13If you divide 2 by 5, the remainder will be 2.
00:09:16Divide this by 5.
00:09:18How much will you get? 1.
00:09:19Divide this by 5.
00:09:21How much will you get? 4.
00:09:23But if you look here,
00:09:25your 5 cuts it completely.
00:09:27And if any number is cut,
00:09:29how much will be the remainder?
00:09:31The remainder will be 0.
00:09:33Similarly, 5 is coming in 6 factorial,
00:09:35which will be cut.
00:09:37So how much will be the remainder? 0.
00:09:395 will also come in 7 factorial.
00:09:41How much will be the remainder? 0.
00:09:435 will also come in 8 factorial.
00:09:45How much will be the remainder? 0.
00:09:46Similarly, 5 will come in every next factorial.
00:09:48And 5 will come in every next factorial.
00:09:50So 5 will be cut from 5.
00:09:52And 5 will be cut from 5.
00:09:54So how much will be the remainder? 0.
00:09:56Okay, now you add all these people.
00:09:58So either you will cut it like this.
00:10:00Sir, how to divide this?
00:10:02By 5.
00:10:04So 4 and 1, 5 will be cut.
00:10:062 and 1, 3 will be the answer.
00:10:08Either write like this.
00:10:10Or else you have to write like children.
00:10:12So 4, 1, 5, 5, 2, 7, 7, 1, 8, 8 came.
00:10:14But 8 is bigger than 5.
00:10:16So how much will be the remainder?
00:10:18So 3 will come.
00:10:20So where my brother came 5 factorial,
00:10:22all the numbers after that
00:10:24give us 0 remainder.
00:10:26All the numbers give us 0 remainder.
00:10:28Similarly, if we talk in this question,
00:10:30we had to divide by 15.
00:10:3215 means 3 and 5.
00:10:343 and 5.
00:10:36And from where will we get 5?
00:10:38From 5 factorial.
00:10:40In 5 factorial, we will get 5 and 3.
00:10:42In 6 factorial, we will also get 5 and 3.
00:10:44In 7 factorial, we will also get 5 and 3.
00:10:46So from here,
00:10:48if everyone's remainder is 0,
00:10:50then if you see here,
00:10:52then you will say that
00:10:54all the remaining numbers have 0 remainder.
00:10:56So add the remaining numbers.
00:10:5824, 36, 32 and 1.
00:11:00How much will be my brother?
00:11:0233.
00:11:04Divide this by 15.
00:11:06Remainder will be 3.
00:11:08The work is over.
00:11:10Understood?
00:11:12Clear?
00:11:14Understood.
00:11:17Hmm.
00:11:19After that, my brother,
00:11:21let's go to the next question.
00:11:23And let's do question no. 62 here.
00:11:25You see here
00:11:27what is said in question no. 62.
00:11:29Here you have been told
00:11:31that 1 power is 1.
00:11:33After that, 2 square is here.
00:11:35After that, 3 cube is here.
00:11:37And doing like this,
00:11:39doing, doing, doing, doing, doing, doing,
00:11:41so my brother, we have 100 powers.
00:11:43And what do we have to do?
00:11:44So we have to divide them by 4.
00:11:46We have to divide this by 4.
00:11:48We have to divide this by 4.
00:11:50We have to divide this by 4.
00:11:52And if you see, my brother,
00:11:54like here the power of 4 will be 4.
00:11:56We have to divide it by 4.
00:11:58We have to divide each incoming number by 4.
00:12:00So what will we get here?
00:12:02Just see here.
00:12:04If you see in this question,
00:12:06then all these numbers have to be divided by 4.
00:12:08I will tell you the most interesting thing.
00:12:10When you divide 1 by 4,
00:12:12it will be 1.
00:12:14When you divide 2 by 4,
00:12:16it will be 4.
00:12:18And when you divide 4 by 4,
00:12:20it will be 0.
00:12:22Here, if you see,
00:12:243, I will take it a little upside down.
00:12:26You assume it like this.
00:12:283 is here.
00:12:30Solve this simple question a little differently.
00:12:32All people are here.
00:12:34You know that when we divide 3 by 4,
00:12:36the remainder will be minus 1.
00:12:38How much will be the remainder?
00:12:40It will be minus 1.
00:12:42And the power of minus 1 is odd.
00:12:44So the remainder will be minus 1.
00:12:46You can also see like this.
00:12:48The cube of 3 is 27.
00:12:50How much is it?
00:12:52It is 27.
00:12:54And when we divide 27 by 4,
00:12:56the remainder will be minus 1.
00:12:58If we divide 4 by 4,
00:13:00the remainder will be 0.
00:13:02And what will happen here?
00:13:04The same sequence will continue.
00:13:06You will say, Guruji,
00:13:08how can it be the same sequence?
00:13:10If you take it a little ahead,
00:13:12you assume it like this.
00:13:14You divide 7 by 7.
00:13:16Or you divide 8 by 8.
00:13:18Okay?
00:13:20And how far will you take the same sequence?
00:13:22You will take the same sequence
00:13:24to the power of 100 by 100.
00:13:26So what will happen?
00:13:28If we look here,
00:13:30you will divide 5 by 4.
00:13:32How much will it be?
00:13:34It will be 1.
00:13:36This whole thing will be divided by 4.
00:13:38Why?
00:13:40You see 6, 6, 6,
00:13:42then after that 6,
00:13:44when we divide by 4,
00:13:462 to this number,
00:13:482 to 3,
00:13:50and 2 to 3.
00:13:52So when nothing is left below,
00:13:54it means that the number is completely decreasing.
00:13:56And when it is decreasing,
00:13:58the remainder will be 0.
00:14:00So what will happen here?
00:14:02Here, 0 will be left.
00:14:04Similarly, we need 4.
00:14:06See, 4 is 2 times 8.
00:14:088 is less than 1.
00:14:10And power of minus 1 will be minus 1.
00:14:128 will be divided by 4.
00:14:14Similarly,
00:14:16there is a pattern in series questions.
00:14:18And you have to understand the pattern.
00:14:20You have to understand the pattern.
00:14:22I understood the pattern in the beginning.
00:14:24But after that,
00:14:26I decided to take you
00:14:28a little further.
00:14:30Actually,
00:14:32the pattern is repeated after every 4 numbers.
00:14:341, 0, minus 1, 0,
00:14:36this is done.
00:14:38Then 1, 0, minus 1, 0,
00:14:40this is done.
00:14:42Then 1, 0, minus 1, 0
00:14:44this is done.
00:14:46And how many groups of 4 people will be formed?
00:14:48One group of 4 people,
00:14:50one group of 4 people,
00:14:52one group of 4 people,
00:14:54so my brother,
00:14:56divide 100 people into 4,
00:14:58so 25 groups will be formed.
00:15:00How many groups are going to be formed?
00:15:0225 groups are going to be formed.
00:15:04But let's see here,
00:15:06what is the value of each group?
00:15:08So here you will see,
00:15:10add all of them.
00:15:12So 1 plus 0 plus minus 1,
00:15:14will be equal to 0.
00:15:16If all the groups are 0,
00:15:18then what will be the overall answer?
00:15:20It will be 0,
00:15:22i.e. option number A is the correct answer.
00:15:24So what we had to do here?
00:15:26We did not have to divide all the numbers here.
00:15:28The pattern formed in 4 numbers,
00:15:30was formed in the next 4 numbers.
00:15:32It was formed in the next 4 numbers.
00:15:34So I took out my answer here.
00:15:36But you say no,
00:15:38it is not like that.
00:15:40So after 4 numbers,
00:15:42I took the next 4 numbers.
00:15:44The pattern is in the same 4 numbers.
00:15:46And after this,
00:15:48the pattern will repeat in the next 4 numbers.
00:15:50One, zero, minus one, zero.
00:15:55So I formed a group of 4 people.
00:15:57The remainder of the group is 0.
00:15:59I will form a group of the next 4 people,
00:16:01and the remainder of the group will be 0.
00:16:03After doing this,
00:16:05there will be 25 groups made out of 4 people.
00:16:07Out of those group, zero will be obtained.
00:16:09And our overall answer will be zero.
00:16:10I am a big fan of you. Thank you Shivamji.
00:16:17Thank you Shivamji.
00:16:47Thank you Shivamji.
00:17:17Thank you Shivamji.
00:17:47Thank you Shivamji.
00:18:17Thank you Shivamji.
00:18:37Thank you Shivamji.
00:18:57Thank you Shivamji.
00:19:27Thank you Shivamji.
00:19:47Thank you Shivamji.
00:20:17Thank you Shivamji.
00:20:47Thank you Shivamji.
00:21:17Thank you Shivamji.
00:21:47Thank you Shivamji.
00:22:07Thank you Shivamji.
00:22:37Thank you Shivamji.
00:23:07Thank you Shivamji.
00:23:37Thank you Shivamji.
00:23:57Thank you Shivamji.
00:24:17Thank you Shivamji.
00:24:47Thank you Shivamji.
00:25:07Thank you Shivamji.
00:25:27Thank you Shivamji.
00:25:47Thank you Shivamji.
00:25:57Thank you Shivamji.
00:26:07Thank you Shivamji.
00:26:27Thank you Shivamji.
00:26:37Thank you Shivamji.
00:26:47Thank you Shivamji.
00:27:07Thank you Shivamji.
00:27:17Thank you Shivamji.
00:27:27Thank you Shivamji.
00:27:47Thank you Shivamji.
00:28:07Thank you Shivamji.
00:28:27Thank you Shivamji.
00:28:47Thank you Shivamji.
00:29:07Thank you Shivamji.
00:29:27Thank you Shivamji.
00:29:47Thank you Shivamji.
00:30:07Thank you Shivamji.
00:30:27Thank you Shivamji.
00:30:47Thank you Shivamji.
00:31:07Thank you Shivamji.
00:31:27Thank you Shivamji.
00:31:47Thank you Shivamji.
00:32:07Thank you Shivamji.
00:32:27Thank you Shivamji.
00:32:47Thank you Shivamji.
00:33:07Thank you Shivamji.
00:33:27Thank you Shivamji.
00:33:47Thank you Shivamji.
00:34:07Thank you Shivamji.
00:34:27Thank you Shivamji.
00:34:47Thank you Shivamji.
00:35:07Thank you Shivamji.
00:35:27Thank you Shivamji.
00:35:47Thank you Shivamji.
00:36:07Thank you Shivamji.
00:36:27Thank you Shivamji.
00:36:47Thank you Shivamji.
00:37:07Thank you Shivamji.
00:37:27Thank you Shivamji.
00:37:47Thank you Shivamji.
00:38:07Thank you Shivamji.
00:38:27Thank you Shivamji.
00:38:47Thank you Shivamji.
00:39:07Thank you Shivamji.
00:39:27Thank you Shivamji.
00:39:47Thank you Shivamji.
00:40:07Thank you Shivamji.
00:40:27Thank you Shivamji.
00:40:47Thank you Shivamji.
00:41:07Thank you Shivamji.
00:41:27Thank you Shivamji.
00:41:47Thank you Shivamji.
00:42:07Thank you Shivamji.
00:42:27Thank you Shivamji.
00:42:47Thank you Shivamji.
00:43:07Thank you Shivamji.
00:43:27Thank you Shivamji.
00:43:47Thank you Shivamji.
00:44:07Thank you Shivamji.
00:44:27Thank you Shivamji.
00:44:47Thank you Shivamji.
00:45:07Thank you Shivamji.
00:45:27Thank you Shivamji.
00:45:47Thank you Shivamji.
00:46:07Thank you Shivamji.
00:46:27Thank you Shivamji.
00:46:47Thank you Shivamji.
00:47:07Thank you Shivamji.
00:47:27Thank you Shivamji.
00:47:47Thank you Shivamji.
00:48:07Thank you Shivamji.
00:48:37Thank you Shivamji.
00:48:47Thank you Shivamji.
00:48:57Thank you Shivamji.
00:49:17Thank you Shivamji.
00:49:37Thank you Shivamji.
00:49:57Thank you Shivamji.
00:50:17Thank you Shivamji.
00:50:37Thank you Shivamji.
00:50:57Thank you Shivamji.
00:51:17Thank you Shivamji.
00:51:37Thank you Shivamji.
00:51:57Thank you Shivamji.
00:52:17Thank you Shivamji.
00:52:37Thank you Shivamji.
00:52:57Thank you Shivamji.
00:53:17Thank you Shivamji.
00:53:37Thank you Shivamji.
00:53:57Thank you Shivamji.
00:54:17Thank you Shivamji.
00:54:37Thank you Shivamji.
00:54:47Thank you Shivamji.
00:54:57Thank you Shivamji.
00:55:25Thank you Shivamji.
00:55:35Thank you Shivamji.
00:55:45Thank you Shivamji.
00:56:05Thank you Shivamji.
00:56:25Thank you Shivamji.
00:56:45Thank you Shivamji.
00:57:05Thank you Shivamji.
00:57:25Thank you Shivamji.
00:57:45Thank you Shivamji.
00:58:05Thank you Shivamji.
00:58:25Thank you Shivamji.
00:58:45Thank you Shivamji.
00:59:05Thank you Shivamji.
00:59:25Thank you Shivamji.
00:59:45Thank you Shivamji.
01:00:05Thank you Shivamji.
01:00:25Thank you Shivamji.
01:00:45Thank you Shivamji.
01:01:05Thank you Shivamji.
01:01:25Thank you Shivamji.
01:01:45Thank you Shivamji.
01:02:05Thank you Shivamji.
01:02:25Thank you Shivamji.
01:02:53Thank you Shivamji.
01:03:13Thank you Shivamji.
01:03:33Thank you Shivamji.
01:03:53Thank you Shivamji.
01:04:13Thank you Shivamji.
01:04:33Thank you Shivamji.
01:04:53Thank you Shivamji.
01:05:13Thank you Shivamji.
01:05:33Thank you Shivamji.
01:05:53Thank you Shivamji.
01:06:13Thank you Shivamji.
01:06:33Thank you Shivamji.
01:06:53Thank you Shivamji.
01:07:13Thank you Shivamji.
01:07:33Thank you Shivamji.
01:07:53Thank you Shivamji.
01:08:13Thank you Shivamji.
01:08:33Thank you Shivamji.
01:08:53Thank you Shivamji.
01:09:13Thank you Shivamji.
01:09:33Thank you Shivamji.
01:09:53Thank you Shivamji.
01:10:13Thank you Shivamji.
01:10:33Thank you Shivamji.
01:10:53Thank you Shivamji.
01:11:23Thank you Shivamji.
01:11:43Thank you Shivamji.
01:12:03Thank you Shivamji.
01:12:23Thank you Shivamji.
01:12:43Thank you Shivamji.
01:13:13Thank you Shivamji.