Question

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

a. 37

b. 35

c. 33

d. 31

Answer 1

Answer: 31

Step-by-step explanation:

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

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