JT Paper 1 Previous Year Math Question Discussion | FACTOR & MULTIPLE

[00:01:07]Hello everyone, a very good morning all of you.

[00:01:11]So class that means for the JT JT and both science and arts.

[00:01:32]So easily examin0000 99 UMG UMG 10% extra 10%.

[00:02:26]So, so okayip Okay. So they go Okay.

[00:03:57]Factors and multiple most important factors. So today topic is a factor factors and multiple and multiple number one factors means the number divisible by which numbers Okay. So two divisible and that means And that means that yes, very good. So, so natural number 1 3 1 are 3 3 2's are 6 3 3's are 9 3 4 are 12 and 3 5 8 12 16 M then five 5 10 15 20 etc. And six 1 are 6 12 then 18 then 24 certain number of certain number of that means factor number of multiple.

[00:07:30]So infinite numbers certain number of factors but multiple infinite number of multiple number that mean itself and multiple multiple.

[00:08:09]Yes, very good.

[00:08:14]Four smallest multiple infinite smallest and greatest infinite. Yes, that means the number itself.

[00:08:32]to every number. Number divisible by one number 1 and The smallest factor of every number what number which have to factor is known as what?

[00:09:28]Every number divisible by one. Yes, very good Sarani. Every number is divisible by one. So the one is a common factor of every number.

[00:09:48]But infinite number of the number which have two factor is known as what prime number that is a prime number. And the number which have more than two factor this known this this number is known as composite number. What composite number composite number two is the smallest prime number? Yes. Smallest even prime number.

[00:10:39]This is the smallest and even prime number. Even prime. Smallest even prime and three smallest smallest odd prime.

[00:10:54]Smallest odd prime two is the smallest even prime and three is the smallest composite number. Two is the smallest even prime number. Yes. And three is the smallest odd prime number.

[00:11:11]Sm that is a through question exam.

[00:11:41]HCM and LCM.

[00:11:55]Yes. So highest common factor, lowest common, lowest common multiple that mean.

[00:12:06]So and examiner favorite questions minimum. Okay.

[00:12:40]Okay.

[00:12:55]Okay. Then Okay. And 12 and 24 and so LCM factori So prime factoriin.

[00:13:55]Okay.

[00:14:08]LCM.

[00:14:31]HC only left. That means highest common factor. But it is wrong.

[00:14:48]It is wrong.

[00:14:50]L7 2 into 2 into 2 into 3.

[00:15:15]Okay.

[00:15:19]12 and 24.

[00:15:27]That means factori and 3 the power 1. Okay. Then factorial That means that highest power 33 24 HCF and yes HCF and LCM upper.

[00:16:52]LCM and HCM upper.

[00:16:54]So clear.

[00:17:13]Yes. Okay.

[00:17:19]important appointment the code.

[00:18:11]Okay. So, LCM and HCF and question LCM and HCF question.

[00:18:48]Okay. So next is a number and b is a number.

[00:19:08]If a b are the two number the product of the two number product of the product of two number product of product of two number product of two number is equal to LCM into HCM number.

[00:19:46]Yes, very good. That means A into B is equal to LCM into H CF.

[00:19:58]This is the most important formula.

[00:20:03]Number one of the number. One of the number one of the numberal That means 24 and LCM that is a 72 and HCF then find out an number 36. Okay, very good or anyone simple.

[00:21:15]Foreign speech. Foreign speech. Foreign speech.

[00:21:30]Okay. So simple another number that means.

[00:21:42]So into LCM that means 12 into 72id 24.

[00:22:01]36. Obviously another number is 36.

[00:22:18]Okay. But example find the HCF of the fraction. Okay. Find HCF.

[00:22:39]Sorry. Find the HCF.

[00:22:43]HCF.

[00:22:45]HCF of fraction.

[00:22:48]Then example to fraction 2 by 3 or 8 by 9 or 16 by 81 or and that is my that is 10 by 27 fraction find sorry h find the h of this fraction 2x3 8 by 9 by 81 and 10 by 27 number and HCM but there is 2 by 81.

[00:23:36]Okay. 2 by 2 by 81. Okay. Okay.

[00:23:42]and option option both.

[00:23:54]So, HCF divided by LCM of denominator HCF of numerator.

[00:24:30]Yes. HCM of numerator.

[00:24:34]Numerator divided by LCM of denominator denominator.

[00:24:53]Very good. LCM of numerator LCM of LCM of what? LCM of numerator.

[00:25:24]LCM of numerator divided by HCF. HCF of HCF of denominator.

[00:25:35]Denominator denominator. Clear?

[00:25:58]number fraction LCM find LCM natorm LCM by HCF by LCM HCF of numerator. So 2 the power 1 2 the power 2 the power 3 power 4 the power 1 into 5 And by LCM denominator 3 the 1 3 the power.

[00:27:18]Okay.

[00:27:33]81 right of the nator. Nator LC by HCF of denominator 3 LCM and HCM.

[00:28:19]factor.

[00:28:23]Very good.

[00:28:35]Yeah.

[00:28:44]And soc.

[00:29:01]So number number fraction 1x 3 by 6 2 by 9 and that is a 4 by 27 that is of numerator. ator divided by HCF of denominator.

[00:29:38]Okay. So LCM HCF of numerator LCM of denominator Okay. Okay. Okay.

[00:30:17]LCM of the numerator. So nator 2 the power 2 and 5 and 1 by ncm denator 3 the power 1 3 the power 3 the power 1 into 2 the power 1 3 the power 3 the power 2 and 3 the power 3 hcf LCM 20ID 3. Very good. 20 / 3 and 1.

[00:31:09]Okay. Okay. Next. Next.

[00:31:24]One divided by the common factor of every number of the denominator denominator LCM highest power three highest power 3 into 2 54 1 by 54. So you are right. Very good.

[00:31:58]So that means LCM and HCM.

[00:32:03]Yes or no?

[00:32:06]I hope.

[00:32:18]Okay.

[00:32:24]Question.

[00:32:26]The ratio of The ratio of two number. The ratio of two number is 3 is to four and there ratio and their HCF is HCF is four and question that is a find their find their LCM data number three and >> [snorts] >> number total is two numbers and the LCM. Okay. Very good.

[00:33:34]Very good.

[00:33:41]Three.

[00:33:50]Sorry.

[00:34:00]ratio.

[00:34:23]And three and four easy Okay.

[00:34:55]Yes. Very good.

[00:34:57]Okay. and 12 simple divided by two number into divid product of two number divided by HCM choice 48. So answer 48 clear. Yes.

[00:36:01]live.

[00:36:07]That means I hope fraction.

[00:36:35]Okay.

[00:36:41]Next.

[00:36:57]Okay.

[00:37:00]Data number that is 117.

[00:37:22]Find out B other number. Find out if two number have data number two number has LCM is a 7007 7,700 S is 11 and one of the number is 275 then find the other number that means LCM M into HCF divided by LCM into HCM that means LCM 7,700 that is 117 75 simple 25 that means 38 number 275. Sorry 38. Sorry. Sorry.

[00:38:52]38 38 cancel 25 and 200.

[00:39:09]Wait wait wait wait.

[00:39:12]38.

[00:39:19]38.

[00:39:21]300. 38.

[00:39:25]200 38 38 38.

[00:39:38]Okay. So clear. Okay. So similar question.

[00:39:46]Okay. So question 3008 38.

[00:40:10]Um, you were the right year.

[00:40:30]308.

[00:40:33]Answer 308.

[00:40:37]Because of 25.

[00:40:56]Sorry about that. Sorry. Sorry. But you are right. Okay.

[00:41:02]Next. Next.

[00:41:06]Next question.

[00:41:11]Question.

[00:41:14]Find the greatest number. Find the greatest Find the greatest number.

[00:41:26]Find the greatest number that will divide that will divide 47 91 and 183 H. [snorts] So, so as to leave as to leave the same remainder the same remainder in each case. Same remainder in each case.

[00:42:18]same remainder that means option four.

[00:42:24]Yeah.

[00:42:26]Option option A.

[00:42:33]Option B 7 option C 9t question.

[00:42:48]Find the greatest number. Greatest number that will divide 43. 43 divide, 91 divide and sorry 183 divide and same option.

[00:43:33]Okay.

[00:43:42]Okay.

[00:43:55]remainder.

[00:44:06]Option option. But 183 and 43 91 43 and 91 4us 48.

[00:44:51]Second step 183US 912 43 43us 43US 140. 140.

[00:45:40]HF.chech.

[00:46:12]2 to the power 4 and 3 to the power 1.

[00:46:20]92.

[00:46:27]46.

[00:46:29]46 into 23. 23 into four. Obviously 23 into 4 to the power 2 into 23 power 1 because prime number 14 into 10 into 14 2 into 5 into 14 - 7 into 2 ^ 2 into 7 ^ 5 5 the power 5 the power 1 5 the^ 1 into 7 the power 1 2 the^ 2 into 5 the power 1 into 7 the power 1 So 84 82 83 83 83 23 number Clear.

[00:48:19]Clear everyone. Okay.

[00:48:22]Very good.

[00:48:24]Next question.

[00:48:35]Question.

[00:48:37]The greatest four-digit number.

[00:48:40]The greatest The greatest fourdigit number. The greatest four-digit number which is exactly is exactly exactly divisible by divisible.

[00:49:06]Exactly. Divisible by 12, 15, 20, and 35.

[00:49:15]35.

[00:49:17]So, option 99 96 4. Option B 9820.

[00:49:29]Option C 9660.

[00:49:33]Option D 9 6 0 0.

[00:49:38]So the greatest fourdigit number which exactly divisible by 12 15 20 and 35 greatestdigit numbers.

[00:50:02]So foreign.

[00:50:07]So option by 10.

[00:51:02]Four.

[00:51:08]and divisible divisible divisible and divisible.

[00:51:21]Yes. 9 9. Sorry. 9 660 6.

[00:51:29]Noble.

[00:51:53]four last seven.

[00:52:02]So optible.

[00:52:33]LCM 2 the power into 3 1 and 5 into 7 That means 420.

[00:53:17]Yes. 420 LCM number four99 divide 420 divide 420 divide a p 239 3 9= 0 9 - 3= 6 9= 6cess So next class 11:00 Thank you all of you. Bye-bye everyone.

[00:54:48]Thank you.