Aptitude - Problems on H.C.F and L.C.M - Discussion

If we divide 7 by 2 it gives a remainder of 1.

Either we add or subtract the remainder 1 from 7 the numbers obtained 8 and 6 which is divisible by 2.

How the answer come in this problem, that we have to add or subtract?

Please explain the calculation of H.C.F in detail.

Please explain the method to calculate the HCF with an example.

Thank you @M. V. Krishna.

Thank you @Deepak.

Why should we find HCF? Why not LCM?

Please explain the solution of this question.

Thanks @Krishna.

@Jenifer.

As you see, the question is asking for greatest number which means greatest factor or divisor.

So here we will do HCF/ GCD.

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).