For the greatest value of p that divide each equation we take the HCF of 48,92,140
THEREFORE ANSWER IS 4.
(Thu, Oct 28, 2010 06:18:07 AM)
How to arrive at this equation p(q2-q1)= (91-43) from 43 = pq1 + r;
91 = pq2 + r;
183 = pq3 + r;
(Fri, Oct 29, 2010 01:56:46 PM)
Solving the equations:
(Wed, Dec 15, 2010 11:29:42 AM)
Simply divide each number by 4 the remainder is same for all so the answer is 4.
(Sat, Jan 8, 2011 09:36:17 AM)
Simply try divide to divide each by the options, by this which is exactly divided then that is the answer.
(Wed, Jan 12, 2011 11:04:01 AM)
Acc to the formulae H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given number.
So as per the first formulae the hcf of 183 & 43 is comming 10
n the third no. is 91 so how will 4 be the ans
(Wed, Jan 12, 2011 11:31:15 AM)
I go with same method as shweta and dhanasekar has said in the forum.
(Wed, Jan 12, 2011 05:40:14 PM)
Divide each with each option.
Pankaj Maharaj said:
(Sat, Jan 22, 2011 01:28:53 AM)
Yesss! you sud simply divide and find the ans in quicker way.
(Sun, Jan 23, 2011 09:56:00 PM)
Getting answer is not important but knowing how to approach that answer is important. Thanks for Prashant.
(Sat, Jan 29, 2011 01:56:18 PM)
That is true. Understanding is more important.
(Sun, Feb 6, 2011 12:07:05 PM)
I don't understand why we need to find the difference. Please explain the logic behind it.
(Wed, Feb 9, 2011 07:40:15 AM)
The difference is used to get the common factors between two nos. it will eliminate the uncommon factors.
And at-last we have only to pick up the highest common factor...
you can try with an example for 30 and 10.
factors of (30) = 5,2,3
factors of (10) = 5,2
factors of (30-10) = 5,2
(Tue, Feb 22, 2011 07:22:18 AM)
The difference is taken to analyze the pattern. Amongst the numbers !
Ie each difference tells us that these numbers are multiples of 4 and have the same remainder because all numbers can be divided by 4.
Hence you get 4.
(Mon, Feb 28, 2011 06:05:57 AM)
WHY WE HAVE TO TAKE DIFFERENCE OF THOSE TWO NUMBERS
(Sun, Mar 6, 2011 12:59:01 PM)
SMART WAY OF SOLVING BY @SHWETHA
Yuva Kumar said:
(Sat, Mar 12, 2011 01:51:05 AM)
Dear Sir/madam please expain I could not understand.
R. Ahmad said:
(Sun, Mar 13, 2011 12:58:44 PM)
Why it is used two times 183 nos Explain?
(Mon, Mar 21, 2011 06:31:19 AM)
If you mult 4*3*7 its coming 84 how 4 will be the greatest no please explain me.
(Sat, Apr 30, 2011 02:41:27 PM)
4*3*7 is wrong right one is 4*12 k
(Mon, May 9, 2011 06:43:30 AM)
Why we have to take the difference of those two numbers?
(Thu, Jun 9, 2011 02:51:59 AM)
I'm not clear with any of the above explanation. Can anyone tell me clearly.
Sai Shyam Singh said:
(Thu, Jul 7, 2011 01:33:35 PM)
It is better explained in the following link...check it out
(Tue, Jul 12, 2011 10:17:16 AM)
@Sai Shyam Singh
Thanks,Aftr checking out this website,now m able to clearly understand the division method of calculating H.C.F.
(Tue, Jul 12, 2011 10:37:34 AM)
Why they took the differences of given 3 numbers and then calculated the H.C.F.
Why didn't they simply calculate the H.C.F OF GIVEN 3 NUMBERS.
(Sun, Jul 17, 2011 05:19:47 AM)
@Mini and all friends
If it was just asked to find the HCF of 43,91,183 then simply the Division method or Factorization method had been applied.
But here it is stated that "so as to leave the same remainder in each case", that's why the difference of the numbers is calculated.
(Sat, Aug 13, 2011 08:39:50 PM)
Please tell me which is the perfect explanation.
(Sun, Aug 28, 2011 01:46:29 PM)
@Prashant: thanks for best explanation.
(Thu, Sep 1, 2011 10:56:49 AM)
Thanks prashant for best explanation.
(Thu, Sep 8, 2011 09:42:37 PM)
Well done Prashant.
(Mon, Sep 12, 2011 10:45:34 AM)
Which is the highest five digit number which is equally divisible by 60, 80, and 90 and how to arrive this answer ?
(Wed, Sep 14, 2011 02:36:30 PM)
Why we have to less these numbers?
(Fri, Oct 7, 2011 01:28:46 AM)
Simply because there is no same factor of these no and they don't divide by each other when we divide 91 by 43 there remainder is 5 that is not the divisible of 43. So we take this method to explanation.
(Tue, Oct 11, 2011 08:47:23 PM)
U guys are not understanding the meaning of H.C.F actually...i'll give an example and an explanation!
Highest common factor
Here are the list of prime factors of 24 and 36:
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:
HCF of 24 and 36 is 2 x 2 x 3 = 12
This is the meaning of H.C.F...so simple! :D
Ashish Saini said:
(Wed, Oct 12, 2011 10:05:24 PM)
Thanks my dear parshant.
(Fri, Oct 28, 2011 08:34:36 PM)
Thanks prashanh, good explanation of sum, but I don't know some people are not at all trying to understand the topic first, then it is very easy my dear friends.
(Tue, Nov 8, 2011 07:43:10 PM)
Can any one explain how to identify. Whether the problem is based on HCF or least common multiple. Is there any key words?
(Sat, Nov 19, 2011 08:15:11 PM)
Simply way is divide 43, 81 and 183 by 4 we get the same remainder 3 for all.
(Thu, Nov 24, 2011 08:43:35 PM)
@Prashant, thanks for explanation
Pooja Madrewar said:
(Sat, Dec 3, 2011 11:39:42 PM)
Explain the logic of this solution
(Sun, Dec 25, 2011 10:55:14 PM)
Thanks prashant your explaination is really good...
(Fri, Dec 30, 2011 09:49:10 AM)
No need to difference between them.
Simply take one by one option and divide given number in question (43, 91 and 183) and equate remainder.
No need to difference between them. Okay friends. So simple !
(Wed, Feb 8, 2012 08:58:26 PM)
We take difference as it is very simple for calculation.
(Wed, Feb 15, 2012 04:33:30 PM)
I'm not clear with any one of the above explanation, why we take the difference of those numbers.
(Fri, Feb 17, 2012 01:18:03 PM)
I am not clear please explain the above explanation
Ravi Varma 501 said:
(Mon, Mar 26, 2012 03:31:14 PM)
Swetha and prashanth explanation is good. And abve some are all in kids formulas. . . So dont look others friends.
Here take the difference between the numbers then start dividing.
48/2, 92/2, 140/2
So HCF is [nothing but the highest common factor].
So HCFis 2*2=4.
(Mon, May 14, 2012 10:22:20 PM)
Hey prashant your explanation is too good. Thanks.
Is there more short method to do solve this.
(Tue, May 22, 2012 10:32:07 AM)
Thanks for the clear explanation prasanth.
(Tue, May 22, 2012 09:57:01 PM)
It is very simple
43,91,183 are the 3 numbers
find the diff between them
let divide the 48,92,140,by 2
here common factor is 2*2
answer is 4
(Tue, Jun 5, 2012 05:54:01 PM)
4*22-gives rem 3.
4*45-also gives rem 3.
All three numbers have equal rem 3 satisfies condition given in number. Hence ans is 4.
(Fri, Jun 15, 2012 04:11:35 PM)
How do you know we are to find the h.C.F ?
I seem to be getting so confused.
(Sat, Jun 16, 2012 11:08:36 AM)
The keyword is greatest or largest- if you find these words, we are required to find HCF. If in case you find least or lowest in the problem, we need to find LCM.
Ankur Jindal said:
(Sun, Jun 17, 2012 10:06:59 PM)
If three nos as in this case is 43, 91 and 183 are given then to find HCF the shortest solution is take the diff:
When pratibhan said the common factor is 2 ok this is write but why she multiple two no of 2 whyn't three no of 2 means the result is 8.
(Mon, Oct 1, 2012 12:25:55 AM)
Pratibhan meant, the common thing coming in prime factor list of all 3 nos is 2*2, i.e 4.
(Wed, Oct 31, 2012 11:16:14 PM)
Why we have to take the difference of the numbers please explain?
(Wed, Nov 14, 2012 05:15:14 PM)
Why we have to take the difference of the numbers can you please explain?
(Fri, Dec 28, 2012 01:11:34 AM)
What is different between HCF & LCM?
And what is the meaning HCF & LCM?
(Thu, Jan 24, 2013 08:48:58 PM)
1.The HCF of two or more numbers is the largest common factor of the given numbers. It is the smallest number which divides the two or more given numbers.
The LCM of two or more numbers is the smallest number that is a common multiple of two or more numbers. It is the smallest number which is divisible by two or more given numbers.
Consider two numbers 120 and 144.
Prime factorization of 120 = 2 x 2 x 2 x 3 x 5
Prime factorization of 144 = 2 x 2 x 2 x 2 x 3 x 3
HCF of 120 and 144 = 2 x 2 x 2 x 3 = 24. 24 is the smallest number which divides both 120 and 144.
LCM of 120 and 144 = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720. 720 is the smallest number which is divisible by both 120 and 144.
2.HIGHEST COMMON FACTOR (H.C.F).
LOWEST COMMON MULTIPLE (L.C.M.).
(Wed, Apr 24, 2013 02:22:31 PM)
Why we have to take difference of two number?
T Shyam Sunder said:
(Tue, May 7, 2013 04:43:35 PM)
Why you had taken difference between this numbers?
(Mon, Jun 17, 2013 07:22:53 PM)
What happens if there are only two numbers, instead of three?