Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 26)
26.
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
Answer: Option
Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
Discussion:
38 comments Page 1 of 4.
Harpreet kaur said:
3 years ago
1651 = 13 * 127.
2032 = 2 * 2 * 2 * 2 * 127.
So common is 127.
That's why H.C.f 127.
2032 = 2 * 2 * 2 * 2 * 127.
So common is 127.
That's why H.C.f 127.
(16)
Jaydeep said:
3 years ago
Thank you so much for explaining the answer.
(2)
Nikita said:
4 years ago
HCF = 2037-1657 = 381 and there factors answer is127.
Because we have to find greatest common factor.
Because we have to find greatest common factor.
(6)
Ayushi said:
4 years ago
1st no 1657 - 6 = 1651.
2nd no 2037-5 = 2032 (now, they both get exactly divisible by greatest no.)
the short trick to find HCF: take the difference and see that difference is divisible by these 2 no.(1651 and 2032) or not.
2032 - 1651 = 381.
Factors of 381 = 1,3,127,138.
So, here the ans is 127 which is the greatest divisor of 381.
2nd no 2037-5 = 2032 (now, they both get exactly divisible by greatest no.)
the short trick to find HCF: take the difference and see that difference is divisible by these 2 no.(1651 and 2032) or not.
2032 - 1651 = 381.
Factors of 381 = 1,3,127,138.
So, here the ans is 127 which is the greatest divisor of 381.
(14)
Balu said:
4 years ago
In these type of questions, just cross-check the answers.
Let the number be "X".
1657/X and 2037/X leaves remainders 6 and 5.
Then, Substitute answers in the place of X and.
1657/127 leaves remainder 6.
2037/127 leaves remainder 5.
Then the answer is 127.
Let the number be "X".
1657/X and 2037/X leaves remainders 6 and 5.
Then, Substitute answers in the place of X and.
1657/127 leaves remainder 6.
2037/127 leaves remainder 5.
Then the answer is 127.
(7)
Aayushi said:
5 years ago
This method of finding HCF of two large no. is called Euclid's division lemma, you can check it further on youtube you will then be able to solve the question.
(2)
Vivek said:
6 years ago
How can we find the HCF of Three co-prime numbers? please anyone explain.
Kumar said:
6 years ago
Super explanation, Thanks all.
Rishav said:
7 years ago
Why HCF and not LCM?
Lets see,
We have to find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5.
Forget about 'greatest'.
we need a number 'which divides 1657' and '2037' ie, if that number is 'x', we have the expression as 1657/x with remainder 6 and 2037/x with remainder 5.
Lets write this in the division form (Dividend = quotient*divisor + remainder)
ie, 1657 = q1 * x + 6.
2037 = q2 * x + 5.
Therefore,
1651 = q1 * x.
2032 = q2 * x.
ie, 'x' (our number) is a common 'FACTOR' of 1651 & 2032 (NOT 'Multiple'). [eg. 24 = 12 *2 or 6*4 or 8*3 ... etc. here, 12 & 2, 6 &4, 8 &3 all are factors of 24 and not multiple].
So, we need common factors of 1651 & 2032 and just select the greatest among them(since the question asks for the greatest).
Lets see,
We have to find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5.
Forget about 'greatest'.
we need a number 'which divides 1657' and '2037' ie, if that number is 'x', we have the expression as 1657/x with remainder 6 and 2037/x with remainder 5.
Lets write this in the division form (Dividend = quotient*divisor + remainder)
ie, 1657 = q1 * x + 6.
2037 = q2 * x + 5.
Therefore,
1651 = q1 * x.
2032 = q2 * x.
ie, 'x' (our number) is a common 'FACTOR' of 1651 & 2032 (NOT 'Multiple'). [eg. 24 = 12 *2 or 6*4 or 8*3 ... etc. here, 12 & 2, 6 &4, 8 &3 all are factors of 24 and not multiple].
So, we need common factors of 1651 & 2032 and just select the greatest among them(since the question asks for the greatest).
(3)
Ankit said:
8 years ago
@Jenifer.
As you see, the question is asking for greatest number which means greatest factor or divisor.
So here we will do HCF/ GCD.
As you see, the question is asking for greatest number which means greatest factor or divisor.
So here we will do HCF/ GCD.
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