What is the greatest number which, when it divides 2987, 3755 and 4331, leaves a remainder of 11 in each case?

Correct option is D

Given:

The numbers are 2987, 3755, and 4331.

The remainder when dividing each number by the greatest divisor is 11.

Solution:

2987 - 11 = 2976,  3755 - 11 = 3744,  4331 - 11 = 4320

First, HCF(2976, 3744) using the Euclidean algorithm:

3744 - 2976 = 768

Now, HCF(2976, 768):

2976 ÷ 768 ≈ 3(quotient 3)

2976 − 3 × 768 = 2976 − 2304 = 672

Now, HCF(768,672):

768 - 672 = 96

Now, HCF(672, 96):

672 ÷ 96 = 7(quotient 7)

Thus, HCF(2976, 3744) = 96

Now HCF(96, 4320):

4320 ÷ 96 = 45(quotient 45)

Thus, GCD(96,4320) = 96

Therefore, the greatest divisor is 96