Find the largest number which 615 and 963 leaving remainder 6 in each case.

We have to find the largest number which divides (615 − 6) and (963 − 6) exactly.
Therefore, the required number = HCF of 609 and 957

Resolving 609 and 957 into prime factors, we have:
609 = 3 × 7 × 29
957 = 3 × 11 × 29
Therefore, HCF of 609 and 957 = 29 × 3 = 87
Hence, the required largest number is 87.