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 x 7 x 29
957 = 3 x 11 x 29
Therefore, HCF of 609 and 957 = 29 x 3 = 87
Hence, the required largest number is 87.