Question

Find the largest number which divides 630 and 940 leaving remainders 6 and 4 respectively.

Answer 1

Since 6 and 4 are the remainders, the number must exactly divide the following:
630 − 6 = 624
and
940 − 4 = 936



624 = 2 × 2 × 2 × 2 × 3 × 13
936 = 2 × 2 × 2 × 3 × 3 × 13
H.C.F. of 624 and 936 = 8 × 3 × 13
= 312
So, 312 is the greatest number that divides 630 and 940, leaving 6 and 4 as the respective remainders.