Question

Find the largest no. which divides 630 and 940 leaving remainders 6 and 4 respectively.

Answer 1

$630 - 6 = 624 \\ 940 - 4 = 936$
take HCF of both
$624 = 2 \times 2 \times 2 \times 2 \times 3 \times 13 \\ 936 = 2 \times 2 \times 2 \times 3 \times 3 \times 13$
HCF= ${2}^{3} \times {3}\times 13$
=312
so 312 is that number,which divide 630 and 940 leaving 6 and 4 remainder respectively.