Question

The greatest number which will divide 1277 and 1368 leaving 3 as the remainder in each case is

Answer 1

subtracting 3 from both
1277-3=1274
1368-3=1365
now
$a = bq + r \\ 1365 = 1274 \times 1 + 91 \\ 1274 = 91 \times 14 + 0 \\ so \: 14 \: is \: the \: greatest \: number \: which \: divides \: both$