Question

Find the greatest number that divides 125, 218, 280 and 342 so as to leave the same remainder in each case

Answer 1

To find the greatest common divisor, we may to use the concept of H.C.F.

Let us assume R is the remainder in each case and N is the divisor.

So, (125-R), (218-R), (280-R) and (342-R) will have common factors.

In Mathematics, when two different numbers, say X, Y are divisible by N, then their difference is also divisible by N.

By using above concept,

(218-R) - (125-R) = 93

(280-R) – (218-R) = 62

(342-R) – (280-R) = 62

Now, N is the H.C.F of 93 and 62

93 = 3 x 31

62 = 2 x 31

Therefore, 31 is the greatest number that divides the four given numbers and leaves the same reminder i.e. 1