The largest number which divides 972 and 2016 leaving remainder 15 in each case, is

The correct option is B 87
The greatest number which divides 972 and leaves the remainder as 15, will be 972 – 15 = 957.

The factors of 957 are 3 × 11 × 29.

Now consider 2016,

The greatest number which divides 2016 and leaves the remainder as 15, will be 2016 – 15 = 2001.

The factors of 2001 are 3 × 23 × 29.

To find the greatest number that divides the two numbers, we will find the Highest Common Factor.

957 = 3 × 11 × 29

2001 = 3 × 23 × 29

∴ HCF of 957, 2001 is 3 × 29 = 87

Thus, the greatest number that divides 972 and 2016 by leaving 15 as a remainder is 87.

Hence, the correct answer is option (b).