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.