Find the greatest number which divides 615 and 963, leaving the remainder 6 in each case.

First we subtract the required remainder from 615 and 963.
Thus, we will get 609 and 957.
609 = 3 × 7 × 29 = 3¹ × 7¹ × 29¹
165 = 3 × 11 × 29 = 3¹ × 11¹ × 29¹
HCF = 3¹ × 29¹ = 87
Hence, the greatest number which divides 615 and 963, leaving the remainder 6 in each case is 87.