Number System 30
Transcript
00:00Jai Hind, Dosto Swagat hai aapka aapke apne bariwaar mein, kaise hain aap log?
00:30Good Evening Bhai, Good Evening sabhi ko, Good Evening
00:35Kaise hain, baniya hai, aap log mast hai, swast hai, batao bhai
00:41Chaliye
00:43Anita, Sapna Kumari, Poonam Kumari, Ekta Sangwan, Rupesh, ITO, Jatin, bahot baniya baat bhai
00:52Chaliye sabhi log live hai, bahot achche bhai, thek hai
00:56Toh, last class mein hum logon ne question number 8 tak kar liya tha
01:00Aur sum of factor kya hota hai, total ka sum of factor kya hota hai, even ka sum of factor kya hota hai, odd ka
01:06Yaha tak mene aap log ko baate kaafi vistrit roop se jo hai, wo bata rakhi thi
01:11Ab hume thoda sa question mein aage barna hai aur aage ki sabhi bhaagon ko dekhna hai
01:14Ki aage ke sawalon ko hum kaise laga sakte hain aur kaise yaha par bana sakte hain
01:18Toh agar aap yaha par dekhenge toh question number 9 mein kya kaha gaya hai, zara padiye
01:22Isme kaha gaya, find the sum of odd divisor of yaha par itna hai
01:26Iska odd divisor ka sum jo hai, wo hume pata karna hai
01:29Aapko humne mere bhai jo hai, total ka, odd ka, even ka
01:33Sabka jo mere bhai sum hai, wo humne yaha par aapko bata rakha hai
01:37Toh aap yaha par kaise nikaloge, toh seedha bologe, sir pehle yaha par ye jo diya gaya hai na
01:4115, 87 aur 60, toh pehle yaha par iske factor banao
01:46Jab aap iske factor banaoge, toh 15, 87, 60 humara lagba kis se katega
01:49Toh agar hum yaha dekhenge toh dekho, ye wali jo value hogi mere bhai yaha par ye 15, 87 aur 15,876 into kitna ho jayega 10
02:0015,876 kya kahin par kisi ka cube hai?
02:03Kya lag raha hai mere bhai aapko? 15,876 kisi ka cube hai, nahi hai?
02:07Thodasa yaad karte hain, thodasa mere bhai yaha par sumashte hain, kis ka hoga, kya hoga?
02:11Yaad karo mere bhai 15,876, kya aapko kisi ka cube nazara raha hai? Aur agar aa raha hai toh kiska hai? Zara batao yaha pe
02:24Batao
02:29Aur agar cube nahi hai toh isko hum factor mein kaise thodenge?
02:33Chaliye mere bhai
02:35Toh subse pehle yaha par 15,625 jo hota hai, wo mere bhai 25 ka hota hai, ye kisi ka aapka cube nahi banega
02:42Aur agar ye nahi banega toh hum isse kaise thodenge?
02:45Agar aap yaha par dekhoge toh aakhari ke jo 2 digit hai mere bhai yaha par, ye aakhari ke 2 digit aapke 4 se karte hain
02:52Aur uske baad me agar hum dekhenge, toh 5 aur ek 6, aur uske baad me 8, 7, 15 mere bhai 3 se katega
02:57Toh yaani 12 se hum iske agar bifurcate karte hain, aur 12 se agar hum isse thodte hain, toh 12 kai guna 12 ho jayega
03:0338 ho chuka hai, 3 baar me 36 ho jayega, uske baad me 27, 2 baar me 24 ho jayega
03:08Phir yaha par kul mila karke phir mere bhai 3 baar me ho jayega
03:13Agar hum 1323 ki baat kare mere bhai, toh ye further humara jo hai wo 3 se katega
03:183 se katega toh kitni baar me? 4 baar me, 4 baar me, 1 baar me
03:22Toh agar hum yaha dekhenge na, toh jaise ye 12 hai, ye 12 ko hum kya likh sakte hain? 4 into 3
03:27Toh 4 ka matlab yaha par 2 ka square into hum likhenge, yaha par 3 likhenge
03:30Uske baad me yaha par hum ye 3 likhenge, ye 21 ka square hai
03:3521 ka matlab yaha par 3 ka square into mere bhai 7 ka square ho jayega
03:39Aur ye 10 ke liye mere bhai hum 2 into 5 likhenge
03:42Toh iss tarike se kul mila karke 2 ke power dekho, toh 2 ke 2 power yaha par hai, aur 1 power yaha par hai
03:47Toh 2 ke humare kitne power ho jayenge? Toh 2 ke humare 3 power ho jayenge
03:52Clear ho gaya ye baat yaha par, 3 ke 2, 1 3 aur 1 4 power mere bhai yaha par ho jayenge
03:57Toh ye humare 3 ke 4 power ho jayenge
04:00Agar hum uske baad me yaha par baat karte hain, toh 5 ka 1 aur 7 ke 2 power hai, toh 5 ka 1 aur mere bhai 7 ke 2 power ho jayenge
04:07Ab agar hum isme dekhenge toh humse question me kaha gaya hai, sum of odd divisor
04:11Jitne bhi iske odd factor honge, un sabhi ka kya batana hai?
04:14Toh un sabhi ka mere bhai yaha par jo hai, wo hume sum batana hai
04:18Toh agar in logon ka jo hai, agar hume yaha par sum hi batana hai
04:21Toh hume yaha par jo sum hai, wo hume kaise batayenge?
04:24Toh inka sum batane ke liye siddhi si baat hai, agar hume odd nikal rahe hain, toh hume even ko consider nahi karenge, baaki sabhi logon ko dekhenge
04:31Toh even ko consider nahi karenge, toh yaani 3 ka 0 ho jayega, 1 ho jayega, 2 ho jayega, 3 ho jayega mere bhai aur kitna ho jayega, toh 4 ho jayega
04:405 ke agar hum power ko mere bhai baat karte hain, toh 5 ka power 0 ho gaya, 5 ka power yaha par 1 ho gaya
04:46Agar hum 7 ki baat karte hain, 0 ho jayega, 1 ho jayega, aur kitna ho jayega, 2 ho jayega
04:52Overall agar hum dekhenge, toh hum yaha par bolenge, sir yeh 1 hai, yeh 3 hai, 3 ka 3 guna 9 hai, 9 ka 3 guna 27 hai, 27 ka 3 guna 81 hai
05:02Uske baat agar hum idhar baat karte hain, toh yeh humara 1 ho jayega aur yeh humara 5 ho jayega
05:07Agar hum idhar baat karte hain, toh 1 ho gaya, 7 ho gaya aur yeh mere bhai, 69 ho jayega
05:12Agar hum sabhi sankhyaon ko jodenge, toh 81 aur 9 humara 90 hai, 90 aur 30, 120 aur 1 mere bhai, 121 ho gaya hai
05:19Agla agar hum dekhenge, toh 6 ho jayega aur yeh humara 57 ho jayega
05:23Aap chaho toh digital sum ke maadam se match bhi kar sakte ho, aur agar aap chaho mere bhai, toh sab ko multiply karke apna ek answer bhi nikal sakte ho
05:31Agar aap sab ko multiply karoge, toh aap yahaan bologe, sir 6, 6, 2, 9, 12 aur yahaan par 726
05:36726 ko 57 ke saath me multiply karna hai
05:40Toh agar hum dekhenge, toh 726 ko 57 ke saath me multiply kare, kya milega, 7 x 6, 42 ka 2
05:484 mere bhai ho gaya pass me, 14 aur 30, 14 aur 30, toh 30 aur 14, kitna ho gaya, 44, 44, 48 ka 8 mere bhai, 4 pass me
05:58Agar hum dekhenge mere bhai, toh yeh humara 49 ho jayega, aur yeh humara 10
06:0249, 10, 69, 69 aur 4 mere bhai, 63 ka 3 mere bhai, 6 humara pass me
06:06Agar hum yahaan dekhenge, toh bolenge, sir 35 aur 6 humara kitna ho jayega, 41, 4, 1, 3, 8, 2
06:12Yahaan par mere bhai, kuch is prakaar se jo hai, wo hamara option aa raha hai, ek baar aap log multiply karke check kari
06:18726 ko agar hum 57 ke saath me multiply karenge, 41, 382, yeh humara bilkul sahi uttar aayega
06:27Jo ki mere bhai, door door tak option me nahi hai, na A hai, na B hai, na C hai, toh kahi answer hoga mere bhai, option number jo D hai, wo humara bilkul sahi uttar hoga
06:37Samajh gaye hain aapar, koi dikkat ki baat ho, toh mujhe bata dijiye bhai
06:40Toh jab bhi agar aapko odd factor nikalna hota hai, sum of odd factor ka nikalna hota hai, toh aap yahaan par jo hai, ek tariqe se mere bhai kisse consider nahi karoge, toh aap yahaan par mere bhai jo hai, wo even ko consider nahi karoge
06:55Ek bachcha keh raha hai, aapne 10 ko chhod diya, agar 10 chhoda hota toh 5 kaan se aata, nahi chhoda hai maine, thekhe
07:02Vishwajit Chatterjee, maine 10 nahi chhoda hai, 10 jo hota hai, wo 2 aur 5 se banta hai, 5 yahaan liya hai, 2 yahaan liya hai
07:09Aajiye chaliye, next question no. 10 dekhiye, jo ki CDS 2023 mein aap logon ke liye poocha gaya, aur yahaan par kya kaha gaya, zara padhiye
07:17Question no. 10 mein hum se yeh kaha gaya hai, ki consider the following statement in respect of all factor of 360
07:24The number of factor is 24, the sum of factor is itna
07:26Kya yeh baat satya hai? Kehne ka matlab yahaan par yeh hai, ki 360 ke sabhi gunan khandon ke sandarma mein nimlikit katno par vichar kariye
07:36Ki kya iske gunan khandon ke sankhya itni hai, aur kya sabhi gunan khandon ka yog hamara itna hai
07:41Kya dono baatein satya hai, ya pehli satya hai, dusri khatam hai, ya dusri satya hai, pehli khatam hai, kya satya hai mere bhai yahaan par, yeh bata diye
07:49Aap yahaan par bolenge, sir dekhe 360 jo hota hai, wo yahaan par 36 x 10 hota hai
07:5336 ko hum yahaan 4 x 9 likh sakte hai, aur 10 ko yahaan par 2 x 5 likh sakte hai
07:594 jo hoga mere bhai, yahaan par yeh 2 ka square ho jayega
08:022 ke 2 power mein, 2 ke 1 power ko jodenge, to yeh 2 ke humare 3 power mein convert ho jayenge
08:07Agar hum 9 ko baat kare, to yeh 3 ka square ban jayega, aur yeh hamara 5 ka 1 power ho jayega
08:12Agar hum yahaan par dekhe, to hum consider kariye aap yahaan par, consider kariye mere bhai, kya hai?
08:18To sabse pehli baat yahaan par aapko number of factor dekhna hai
08:20Number of factor ko nikalne ke liye, power mein ek ek badha karke guna karte hain
08:253 mein ek badha denge, 4 aa jayega
08:27Uske baad yahaan par 2 mein ek badha denge, 3 aa jayega
08:30Uske baad ek mein ek badha denge, 2 aa jayega
08:32Yeh mila karke 24 ho jayega
08:34Yeh kitna ho jayega?
08:36To 24 ho jayega yahaan par
08:38Uske baad agar hum dekhenge, to yahaan par sum of a factor
08:41Sum of factor ki agar hum baat kare
08:43To factor ka sum nikalne hai, to yahaan par yeh poore ka mere bhai sum hoga
08:46To jaise agar aap 2 ki hi baat karo, 2 ka power 0, 2 ka power 1, 2 ka power 2 aur 2 ka power mere bhai hoge yahaan par 3
08:55Isko multiply karenge
08:57Uske baad 3 ka mere bhai kahani kya hoga?
08:593 ka power 0, 3 ka power 1 aur 3 ke power mere bhai yahaan par 2 ho jayega
09:04Theek hai, clear hai yeh baat yahaan par
09:06Aur uske baad last mein hum yahaan par kya karenge?
09:08To last mein mere bhai hum yahaan par 5 ke bhi power ko include kar denge
09:12Kyuki sum of factor mein hum yahaan par sabhi logon ko count karte hain
09:14To agar hum yahaan par dekhe to mere bhai 5 ka bhi power 0 aur 5 ka power 1
09:19Yeh aapko dono le karke chalna padega
09:22To agar aap dekhoge to 1, 1 ka double, 2, 2 ka double, 4, 4 ka double, 8 yahaan par
09:27Agar aap yahaan dekhoge to kya bologe?
09:29To aap yahaan bologe 1, 1 ka 3 hona, 3, 3 ka 3 hona, yahaan par 9
09:34Agar aap yahaan dekhoge to 1 aur uske baad mein yahaan par 5
09:37Yeh mere bhai yahaan par clear cut ho jayega
09:39Agar hum dekhe to bolenge 8 aur 4, 12 aur 14 aur 1 humara ho jayega 15
09:42Agar hum yahaan dekhe to 10 aur 3, 13 aur yahaan dekhe to mere bhai ho jayega 6 yahaan par
09:4815 ka 6 guna 90 aur 13 guna 170 matlab yahaan par 1170 yeh humara hoga
09:53To pehla baad kya iske number of factor 24 hain to bilkul 24 hain
09:57Kya iska sum of factor 1170 hain to hanji sum of factor 1170 hain
10:02Matlab iske dono kathan satya hain aur agar dono satya hain mere bhai to option number jo C hain
10:07Wohi humara bilkul sahi uttar hain
10:09Option number jo C hai
10:12Wohi humara kya hain mere bhai yahaan par
10:14To bilkul sahi uttar hain
10:16Ek bachche ka comment dikhaye sir
10:19Sorry for asking karke likha aa raha hai
10:22Bas bas bas
10:24Sorry for asking I believe in you
10:27But please bataye ki aapki saare sheet kaafi hai kya
10:30Rohit swamy bilkul kaafi hai agar hum aapko sheet ke questions de rahe hain
10:34Agar aap classroom sheet aur practice sheet agar aap sirf itni hi karte hain
10:36To bade aasaan tareeke se mere bhai ya paper ko clear kar sakte hain
10:39Aapko kuch aur karne ki awasakta nahi hain
10:42Itna mere bhai apne aapme kaafi hai
10:44Bas aap iski multiple time practice kariye
10:47Lekin aapko dono sheet lagani padegi
10:49Classroom bhi aur aapko practice sheet bhi
10:51Dhyan rakhiye guys baat ka
10:53Aaj ye chaliye
10:55Next question ek 11 number dekhiye kya kaha gaya hai
10:57Bola gaya the sum of even divisor of 4096
11:004096 ke even divisor ka jo hain hume sum batana hai
11:03Ab yaar sabse pehli baat ye 4096
11:06Ye humara kis ka mere bhai
11:08Kya ye kisi ka square hai
11:10Kya hai mere bhai ye kis se karta hai yahaan par
11:12To agar maan lijiye aapko nahi pata hai 4096 kis se karta hai to koi baat nahi
11:164 se agar aap dekhenge to yahaan par jo hai
11:191024 se mere bhai katega ye
11:21Agar aap dekhonege to ye 4 jo hota hai ye 2 ka square hota hai
11:25Aur ye 1024 jo hota hai mere bhai 2 ke 10 power ke barabar me hota hai
11:29Tik hai na to agar aap dekhenge to 2 ka square hota hai
11:31Tik hai na to agar aap dekhenge to 2 ka 10 power 2 ka 2 power
11:34Yaani ye 2 ke power mere bhai 12 ke barabar me hota hai
11:37Kis ke barabar me hota hai to 2 ke 12 power ke barabar me hota hai
11:412 ke kis ke barabar me hota hai to 2 ke 12 power ke barabar me
11:45Maine jab isko toda to ye 4 into itna me tuta hai
11:48Ye 2 ka square ye 2 ke 10 power 2 ke 10 power 2 ke 2 power
11:512 ke 12 power ke barabar me ye tutega
11:54To agar hum
11:56Kaha gaya sum of mere bhai divisor
11:58To yahaan hum shuru karenge 2 ke 0 power se
12:01Aajaayega 2 ka 1 power
12:03Phir aajaayega 2 ka 2 power
12:05Aur ye silsala mere bhai yahaan par chalta rahega
12:08Aur ye kahaan tak chalta rahega
12:10To ye jo hai na mere bhai yahaan par
12:12Ye humara chalta rahega 2 ke 12 power tak
12:14Tik hai aur mujhe in kya karna hai
12:16Sab ka mere bhai sum nikalna hai
12:18Ab sabse badi baat sum of all factor hota hai
12:20To sum of all factor hota hai
12:22To hum 2 ke power 0 se shuruwaat karte hai
12:24Yahaan sum of even factor bola hai
12:26To even me agar bola gaya hai na
12:28Tik hai 16 ka cube hai to wahin baat hai
12:31Aap ekat nahi hai 16 ka cube hai to
12:332 ka power 12 ho jayega
12:35To agar even factor bola hai to
12:37Ye 2 ke power 0 ko aap consider nahi karenge
12:39Agar aap consider nahi karenge
12:41To ab aapke saamne kya ho jayega
12:43Aap bolenge ye 2 hai
12:452 ka square 4 hai
12:47Mere bhai yahaan par ye 8 hai
12:49Aur aise karte karte karte karte karte
12:51Last me yahaan par 1024 hai
12:53Agar aap sahi maine me dekhoge
12:55To ye ek geometric progression hai
12:57Ye kya hai mere bhai yahaan par
12:59Radha ji tabse keh rahi hai
13:01Ye kaam karahein
13:03Agar aap mal lejiye isko aap likhti hai
13:0516 ka cube
13:07Radha ji aap ek baat bataiye
13:09Ye jo 16 hota hai ye 2 ka power 4 nahi hota hai
13:11Aur 2 ke power 4 ka power 3
13:13Matlab yahaan par 2 ka power
13:154 x 3 yahaan 2 ke power
13:1712 ke barabar mein hoga
13:19To galat kaha hai yahaan par ye bataiye
13:21To isliye maine isko 2 ka power kitna likht diya hai
13:2312 likht diya hai
13:25Ab kaafi sare log hote hai
13:27Jo isko is tarikay se mere bhai sum karte hai
13:29Ki yahaan par 2 jodenge
13:31and we will see that this is a geometric progression.
13:35Geometric progression means that here the second number is some times of itself.
13:41For example, this is double of this, this is double of this, this is double of this, this is double of this.
13:45In this way, my brother, by doing here, okay?
13:49So, here this geometric progression happens, so what is the sum of this?
13:53You tell me once, because the whole formula of this, the whole concept,
13:57my brother, we have told you everything in the formula book.
13:59Like the sum of infinite terms, which happens in any geometric progression,
14:03is 1 upon 1 minus r.
14:05But this, my brother, is not up to infinite,
14:07this is not up to infinite,
14:09my brother, it is up to 12 terms.
14:11One first number, second number, third number, fourth number.
14:13So, my brother, sum of n terms.
14:15So, the sum of n terms,
14:17which happens in any geometric progression,
14:19my brother, what happens here?
14:21You tell me here quickly.
14:23Quickly, my brother, tell me here,
14:25it will be 4096,
14:27where in the last, okay, my brother,
14:29you write 4096,
14:31it will not make any difference,
14:33the ultimate difference that is going to happen,
14:35it is going to happen from the number of terms.
14:37Like this, it becomes 1, 2, 3, 4,
14:39in this way, in total,
14:41my brother, here 2 becomes 12.
14:43So, you tell me here,
14:45what is the sum of geometric progression
14:47here?
14:49If anyone knows, then?
14:51If you do not know, then no problem,
14:53we will tell you here.
14:55Understood?
14:57In the formula book,
14:59Arithmetic progression,
15:01Geometric progression,
15:03Harmonic progression,
15:05what is the first term,
15:07what is the difference here,
15:09and we have told all these things.
15:11A child is telling n into n plus 1
15:13into 6n plus 1 by 2,
15:15which is completely wrong,
15:17we will not be able to apply it here,
15:19how many of you know these things?
15:21You cannot apply the series of AP,
15:23you understand this thing here,
15:25this is not a natural number.
15:27When does AP apply?
15:29When there is equal add or equal subtract.
15:31In add and subtract, AP is applied,
15:33in multiply and divide, GP is applied.
15:35Here, every number is becoming double,
15:37so here, my brother,
15:39we will apply the concept of GP.
15:41Tell me,
15:43this plus n minus 1 into d,
15:45what are you forgetting?
15:47My brother,
15:49whatever you are saying,
15:51does anyone know what you are saying?
15:53A child has got the right answer,
15:55he is crying.
15:57Actually, what happens here,
15:59this becomes equal to
16:01A into R power,
16:03R power n minus 1 divided by
16:05R minus 1,
16:07and this happens on condition
16:09when R value is greater than 1,
16:11and if here R value is less than 1,
16:13then this story will completely reverse.
16:15Understood?
16:17This is the story of AP,
16:19that is, the story of GP.
16:21A tells about the first term,
16:23R tells about the common ratio.
16:25So here,
16:27either you add all of them,
16:29this is the option you have,
16:31or else, my brother,
16:33you multiply all of them.
16:35So if we apply the same formula here,
16:37then instead of A,
16:39we will take the first term,
16:41that is, we will take 2.
16:43Common ratio means
16:45how many times this number is multiplying itself.
16:47So as it is multiplying itself twice,
16:49it is multiplying itself twice,
16:51it is multiplying itself twice.
16:53To subtract R,
16:55divide the second term by the first term.
16:57If you divide 4 by 2 or 8 by 4,
16:59then the value of R will be this much.
17:01n means how many digits are there here.
17:031, 2, 3, by doing this,
17:05there are a total of 12 digits.
17:07Minus here will be 1,
17:09and how much will be below,
17:11if we see here,
17:132 into,
17:15subtract 1 from 12,
17:172 power 12 is 4096.
17:192 power is 4096.
17:21If we subtract 1 from 4096,
17:23then it will be 4095.
17:25How much will be here,
17:27then you will say,
17:29it will be 4095.
17:31Did you understand what I said?
17:33Subtract 1 from 4096,
17:35it will be this much,
17:37and subtract 1 from 2,
17:39then the value of 40 will be 80,
17:41and the value of 95 will be 190.
17:43The answer will be 8190.
17:45Option no. B for Bahubali is the correct answer.
17:47Option no. B for Bahubali is the correct answer.
17:49If I tell you a small thing,
17:51if you go to sum this,
17:53if you add everyone,
17:55your life will be ruined.
17:57As soon as you see here,
17:59there is a geometric progression,
18:01there is a series of numbers,
18:03immediately you apply the formula of GP,
18:05and you get the answer in just two lines.
18:07So the first thing you have to clear
18:09is what is AP and what is GP.
18:13Now look at question no. 12.
18:15Sum of even factor of 1800.
18:17We are not going to tell you this question.
18:19How to find the even factor of 1800 here?
18:21I think you understand it very well here.
18:23I think you understand it very well here.
18:25And you can clear these things here.
18:27And you can clear these things here.
18:29There is nothing to worry about here.
18:31There is nothing to worry about here.
18:37There is nothing to worry about here.
18:39There is nothing to worry about here.
18:41Is it clear?
18:43Let's talk about the next question.
18:45And the next question is question no. 13.
18:47It is from CDS, 2022.
18:49It is said that you consider here
18:51that there is a number called N.
18:53In this, the number of odd factors
18:55is 60.
18:57The number of even factors
18:59of N is 720.
19:01What is it?
19:03And whatever it is,
19:05it is the truth.
19:07If we talk about it,
19:09first of all,
19:11if we talk about N,
19:13what is the power of 12?
19:15It is 6.
19:17What is the power of 3?
19:19It is 8.
19:21What is the power of 5?
19:23It is 3.
19:25This is a prime number.
19:275 is also a prime number.
19:29But 12 is not a prime number.
19:31If 12 is not a prime number,
19:33then how will we break it?
19:35We are going to break it in prime factors.
19:37If we break it in prime factors,
19:39then 12 will be
19:41the square of 2,
19:43that is, 4
19:45multiplied by 3.
19:47And what is its power?
19:49It is 6.
19:518 multiplied by 3.
19:53If we want to break 12,
19:55then 12 will be 4 multiplied by 3.
19:574 is the square of 2.
19:59It is a square.
20:01If we see one more line,
20:03then it is 2.
20:052 multiplied by 6 is 12.
20:073 multiplied by 6 is 6.
20:093 multiplied by 6 is 8.
20:115 multiplied by 6 is 3.
20:13If we see further,
20:15then 2 is the power of 12.
20:176 multiplied by 8 is 14.
20:196 multiplied by 8 is 14.
20:215 multiplied by 5 is 3.
20:235 multiplied by 5 is 3.
20:25If we see all the things,
20:27then here
20:29what is APGP?
20:31Sapna Kirar is asking.
20:33If you want to know about APGP in detail,
20:35then you can search on YouTube.
20:37There will be a single 1.5 hour video
20:39in which all the things will be told to you.
20:41If you don't know anything,
20:43then don't miss it.
20:45You get all the information.
20:47Like if we see,
20:49if you want to know about APGP,
20:51Sapna ji,
20:53you don't have to do anything.
20:55If you run YouTube,
20:57then after going to YouTube,
20:59you can search here.
21:01APGP by Aditya Ranjan Sir.
21:03You will get it here.
21:05APGP by Aditya Ranjan Sir.
21:07You will get it here.
21:09And you can see
21:11Sapna ji from here.
21:13There is no problem.
21:15A video will pop up in front of you
21:17about Saman Antar Srini
21:19and Earth Progression.
21:21This is a 2 hour video
21:23in which AP is told.
21:25If you want to read GP,
21:27then this is a 2 hour video
21:29in which GP is told.
21:31So you can read from here.
21:33You can learn all the questions.
21:35You can know and understand.
21:37Now if we talk here,
21:39then see what is said here.
21:41First of all,
21:43if we have to find the number of factors,
21:45then what do we do?
21:47We multiply everyone by 1.
21:49If we have to find the even factor,
21:51then in the case of even,
21:53we will not increase it.
21:55If we are finding the even factor,
21:57then we will not increase it in even.
21:59If it is 12, then we will write 12
22:01and increase it in the rest of the people.
22:03We will multiply 14 by 15 and 3 by 4.
22:0512 x 15 will be equal to
22:07180 x 4 will be equal to 720.
22:09This is done.
22:11If we have to find the odd number of factors,
22:13then remember
22:15that you will not consider
22:17the even factor in the odd.
22:19If we do not do it,
22:21then if it is 14,
22:23then it will be 15.
22:25If it is 3, then it will be 4.
22:27If it is even, then it will be 720.
22:29Both are correct.
22:31Option number C is
22:33our correct answer.
22:35It is our correct answer.
22:37There is no problem here.
22:39You can understand
22:41very well here.
22:43You can know very well
22:45how to find the number of factors,
22:47how to find the number of even factors,
22:49and how to find the number of odd factors.
22:51We have taught you everything here.
22:53We have asked you 6 types of questions.
22:55Total number of factors,
22:57total number of even factors,
22:59total number of odd factors,
23:01sum of factors, sum of even factors, sum of odd factors.
23:03We have taught you these 6 types of questions.
23:05Now here
23:07it is said
23:09what is the sum of reciprocal of factors
23:11360.
23:13If I change this question
23:15a little bit
23:17and change this question
23:19here.
23:21Before knowing this question,
23:23before knowing the sum of reciprocal,
23:25you know this word here.
23:27Product of factor.
23:29First you know the number of factors,
23:31then you know the sum of factors,
23:33now you know the product of factors.
23:35You know the number, you know the sum,
23:37now you know the product of factors.
23:39See question no. 15 directly,
23:41then we will understand the rest later.
23:43Now we want to know about the sum of odd factors.
23:45The product of factors
23:47is equal to
23:49the sum of odd factors.
23:51The product of factors
23:53is equal to
23:55the sum of odd factors.
23:57If we talk about the product of factors.
23:59For example,
24:0112 is equal to
24:0312 is equal to
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24:0712 is equal to
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35:23own
35:27some
35:29some
35:31part
35:33question
35:35question
35:37question
35:39form
35:41form
35:43form
35:45form
35:47form
35:49form
35:51So, before doing that, I will give you some changes in this question and I will give you
35:57data here that if this number was not given here and my brother did not give this number
36:03here, you understand here that this number would not have been given and instead of giving
36:07this number here, only 25 would have been given here that how can you add 25 here in
36:12pairs of 2?
36:13How many ways have you changed all these options here, take my brother, I have changed
36:18all the options here for you that find the number of ways to express 25 as a product
36:24of two factors.
36:25How many ways can you express 25 in the product of two people?
36:32This is our question.
36:33Like I was making you do it in the back, how can you write 24 here?
36:38In this question, I said that 25 is the number of ways to express it in the form of two
36:46ways.
36:47Now, what will you say here?
36:49Sir, if there is 25, then how can the method of writing 25 be written here?
36:55So, first of all, if we talk about 25, then either we can write 1 x 25 or we can write
37:025 x 5 here.
37:03Meaning, how many ways are there here?
37:05So, we have two ways.
37:07How many ways are there?
37:08So, there are two ways.
37:09But is the man going to do this in the paper?
37:12Tell me, will he do this?
37:14What do we do?
37:16We subtract the number of factors and divide it by half.
37:19What do we do by subtracting the number of factors?
37:22We divide it by half.
37:23So, we don't do it like this, my brother.
37:25We see 25 here first.
37:2725 means that there is a square of 5 here.
37:30So, what will we do here?
37:31We will subtract the number of factors.
37:33In the number of factors, you also know that whatever has been given, always add it to
37:37it.
37:38So, this becomes our number of factors.
37:40If there is no other number, then we cannot increase the power in any other number.
37:46Now, this number of factors has come.
37:48But when you move towards your answer, what will you do here?
37:52Will you directly divide it by half?
37:54Tell me, will you divide it by half?
37:56So, you cannot do it.
37:573 cannot be divided by half.
37:59The answer will come in decimals.
38:00So, my brother, when it cannot be divided by half, then remember that whatever number
38:04of factors you have got, add 1 to it and divide it by half.
38:08Otherwise, my brother, if you divide it by half of 4, then how much will it be?
38:11Now you will say, sir, why did you tell me to add 1?
38:13That's why I said, my brother, because if you look at it in reality, then there are only
38:183 factors of 25.
38:1925 is either subtracted from 1, or from 5, or from 25.
38:23Okay, so there are only 3 factors of the poor.
38:26So, there are only 3 factors.
38:27So, what is the number of factors?
38:283 has come.
38:29But when it comes to making pairs, then look, there were 3 people.
38:33Who was who?
38:34There was one.
38:35Okay.
38:36After that, my brother was 5.
38:37How many were there?
38:38There were 25.
38:39One more 25 juggled together.
38:41Poor 5 was left alone, single.
38:44So, when 5 was left alone, single, then who will help him?
38:47So, no one helped him.
38:49That's why he created his duplicate.
38:51And he made a pair with him.
38:54So, that's why, when someone is less, then they make a pair and then what do they do?
39:01They divide.
39:02Remember this, my brother.
39:04So, if we talk about this question here,
39:0611, 0, 25.
39:07So, if we say this, then what is this 11, 0, 25, my brother?
39:11So, this is a perfect square.
39:12However, the case that happens here,
39:14here, the case of adding 1.
39:16So, the case of adding 1 comes in the case of a perfect square.
39:20Because whenever there is a perfect square, then its number of factors always comes as an odd number.
39:25Whenever there is a perfect square, then my brother, the number of factors will come as an odd number.
39:29Okay.
39:30So, this is 11, 0, 25.
39:32If we see here, if we divide it by 25,
39:35so if we divide it by 25, then 25 will be 4 times 100,
39:38102 will be there, then 25 will be 4 times 100,
39:4125 will be there at once.
39:4225 into 41.
39:44If you see 25, then it is a square of 5.
39:46And if you see 41, then it is a square of 21.
39:49The square of 21 means the square of 3 into the square of 7.
39:52So, if we see here,
39:54so what will we say here?
39:56So, we will say here, Guruji, see the number of factors first.
39:58So, what will happen in the number of factors?
40:00Increase 1, after that increase 1 in this as well.
40:03After that, increase 1 in the next as well.
40:05So, how much will be there? 27.
40:06And what did I say, whenever there is a perfect square, the number of factors will be odd.
40:11Whenever there is a perfect square, the number of factors will always be odd.
40:14Like you see, four perfect squares,
40:16take out the number of factors of that number and multiply it.
40:1816 perfect squares,
40:20take out the number of factors of that number and multiply it.
40:22You take out 25, 36,
40:24you take out 81,
40:26whatever perfect square is in the world,
40:28you will take it out here
40:31now you will say sir whose perfect square is this
40:33so 7x3 is equal to 21x5 is equal to 105
40:36this 105 is the whole square of 105
40:38105 is the whole square of 105 that's why the number of factors is so odd
40:41and whenever the number of factors is odd
40:43so when we have to make it a pair
40:45so here we will say
40:47there are 27 people
40:49call one more person
40:50now it will be 28
40:52and 28 will be a pair
40:53so how many pairs will be there?
40:5414 pairs will be there
40:56so what will be the correct answer?
40:57so the correct answer will be option no. B
41:01so what will be the correct answer?
41:02so option no. B will be the correct answer
41:05so whenever this happens
41:07so my brother you have to be careful
41:10you have to add 1 to it and increase the number
41:14ok
41:18now a small question here
41:21a question of miscellaneous
41:22you can see this also
41:24you can solve this easily
41:26miscellaneous means a mixed type of question
41:28a kid is asking what miscellaneous means
41:30miscellaneous means mixed
41:32first question is something else, second is something else, third is something else
41:35where there is no limit
41:39so you can see here
41:40the divisor of the number is exclusive of the number 1 and itself
41:45if I make this question a little easier
41:47and I make this question a little easier for you
41:51ok, now assume that we have removed the question
41:53and I have said here that
41:55you assume that
41:571 my brother here
41:59how do I do this here
42:01assume that this is our number
42:04I will change the question here a little
42:08ok, your question will be changed a little
42:15ok, take this
42:20now I have changed this question a little
42:22and in this question I have said
42:25the number of divisors of 80
42:27how many divisors are there excluding 1 and itself
42:31to say 80 means
42:33you have a lot of factors in the world
42:35ok, so what you do here my brother
42:37tell all the factors
42:39but there should not be 1 and 80
42:41there should not be 1 and 80
42:43so the first thing we tried to figure out here
42:45that this 80 my brother
42:47from whom will it be deducted
42:49and how many times will it be deducted
42:51so if we see here
42:53how many times will it be deducted from 1
42:55so 80 times
42:57if we see here how many times will it be deducted from 2
42:59so you will say sir here
43:01what is going to be deducted from 2
43:03my brother is going to deduct from 40
43:05after that if we see
43:07so will it be deducted from anyone else
43:09so it will not be deducted from 3
43:11how many times will it be deducted from 4
43:13so 20 times
43:15after that will it be deducted from 5
43:17so my brother will deduct from 5 16 times
43:19and it cannot be deducted from any other number
43:21so 4, 5, 16, 20, 40, 80
43:23these are its 8
43:25which are its factors
43:27what is said here
43:29so here it is said my brother
43:31that 80 here
43:33divisor of number 80
43:35exclusive of 1 and itself
43:37don't take 1, don't take 80
43:39now tell the remaining here
43:41so 1, 2, 3, 4, 5, 6
43:43so how many are left my brother
43:45so 6 are left
43:47one way is to write
43:49if we express this thing in another language
43:51so how will we do it here
43:53so we will say here
43:55we are reading the method of prime factorization
43:5780 we have to write
43:5916 into 5
44:0116 means 2 power 4
44:03into 5 power 1
44:05so first of all
44:07what we will do here
44:09we will take out the number of factors
44:11we will increase 1 in 4, it will be 5
44:13we will increase 1 in 1, it will be 2
44:15means how many factors will be there, it will be 10
44:17so remember, once there was a question
44:19what was there in that question
44:21so it was said that all the factors
44:23tell everything except 1
44:25so here we minus 1
44:27I will show you the question here
44:29number of factors except unity
44:31so my brother had a question
44:33number of factors except unity
44:35I will show you the question here
44:37except unity
44:39my brother had said
44:41or in a way here it was said proper factor
44:43if you see here
44:45so while teaching proper factor
44:47I had told you
44:49out of all the factors
44:51we subtract 2
44:532 means first number and last number
44:55the number 1 and itself
44:57remember my brother
44:59I had told you that if you want to get proper factor
45:01out of any number
45:03then subtract 2
45:05one for first, one for 1 and one for yourself
45:07so it is the same thing
45:09here this word was shown as proper factor
45:11and here if we see
45:13so here without saying proper factor
45:15my brother
45:17it was added in an easy way
45:19so what we will say here
45:21we will say ok, let's say
45:23you have 10 factors
45:25let's say
45:274 to 20, 5 to 16
45:29and my brother, will it be subtracted from anyone?
45:31ok, it will be subtracted from 8 into 10
45:33ok wait, sorry
45:35write 8 into 10
45:37I missed this by mistake
45:39I missed this by mistake
45:41write 8 into 10
45:43so according to this, 2, 2, 4, 2, 6, 2, 8, 2, 10
45:4510 factors are there
45:472 people are not to be counted
45:49so 2 people are not to be counted
45:51so my brother, we will count 8 people
45:53so I said, either you write it like this
45:55or you write it like this
45:57where 10 factors are there
45:59and out of 10
46:01my brother, here for 1
46:03subtract a number for this
46:05and one for this
46:07so what will be the answer?
46:09what will be the answer of this question?
46:11it will be 8
46:13I gave you an example
46:15I explained one thing to you
46:17are you understanding what I am saying?
46:19like, either in the question
46:21you say, don't take 1 and itself
46:23in that case, you minus here
46:25or you say, my brother, find the proper factor
46:27in that case also
46:29you have to minus these two
46:31so you have to keep this in mind
46:33so if we see the last question
46:35which was asked in CDS 2018
46:37so what was said in this?
46:39that this number
46:41subtract 1 from its sides
46:43and yourself
46:45so if we see here
46:47what is the solution of 3808?
46:49so the solution of this is
46:51I will divide it
46:53if we divide it by 8
46:55then it will be
46:578 times 4 times 32
46:59then it will be 68
47:018 times 8 times 64
47:03then it will be 40 in 5 times and 1 time
47:05can we divide it by 8?
47:07so you will say, yes, we can
47:09if we divide it by 3
47:11then it will be 16 times
47:13and this will be 17 times
47:1517 times, how will we divide it?
47:177, 6, 13
47:19and 2 out of 13 will be 11
47:21this can be 11
47:23so if we see here
47:25it will be 11 times
47:2751 will come
47:2944 in 4 times and this much in 7 times
47:31then this 147
47:33so if we divide it by 7
47:35then this 147 will be 3 times
47:377 square into 3
47:39like this some things are going to break
47:41now here all these factors
47:43are like this
47:45what can we write 8?
47:47so we can write 8 as 2 cube
47:49this 8 is finished
47:511 power of 3 plus 1 power of 3
47:53will be 2 power of 3
47:55this is also finished
47:577 power will be 2 power
47:59this is also finished
48:01this is also written
48:03now what is our aim?
48:05our aim is to find number of factors
48:07what is here?
48:09we have to find number of factors
48:11so if we talk here
48:13when we see number of factors
48:15then what will be the number of factors?
48:173, 1 plus 2 will be 4
48:192, 1 plus 2 will be 3
48:212, 1 plus 2 will be 3
48:231 plus 2 will be this much
48:254 into 3, 12 into 2, 36 into 2
48:27how much will be? 72
48:29but what is said in question?
48:31in question this line is said
48:33Exclusive of 1 and itself
48:35leave 1 and itself
48:37means here
48:39from 72
48:41subtract 1 and itself
48:43then 70 will be
48:45how much will be?
48:4770 will be here, option number C
48:49will be our correct answer
48:51so now we say 5 into 5
48:53power is 1
48:55so we will multiply by 1
48:57we could not understand your question
48:59it was not clear
49:01we are telling honestly
49:03ok
49:09it is clear here
49:11so whether it is a question of proper factor
49:13or it is a question of
49:15excluding 1 and itself
49:17both are same
49:19and in both number of factors
49:212 will be minus
49:23ok?
49:25so now
49:27we will see the remaining questions
49:29about factor
49:31remaining things
49:33see here
49:35I think you will need one more class
49:37then you will be able to understand
49:39like question number 14
49:41ok
49:43how many questions you have?
49:4514, 17, 18, 19
49:4720, 21
49:49so in total you will need
49:513 more classes
49:53which we will take tomorrow
49:55I think I will be able to finish it today
49:57because it takes a lot of time to explain
49:59so one more factor class
50:01you will take tomorrow
50:03and after that 2 classes or 3 classes
50:05we will make number of 0
50:07like Wednesday, Wednesday, Thursday, Friday
50:09by Friday your topic will be over
50:11whole number system
50:13because first of all
50:15we have studied unit digit, divisibility, remainder
50:17factor is left
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