Question

Find the largest two digit number that divides 673 and 865, leaving remainder 1 in each case. . 91 93 96 98

Answer 1

let the number be x

as x divides 673 and remainder is 1

it must be divide to 672

also , x divides to 865 and remainder is 1

it must be divide to 864

so x divides both 672 and 864

so x is hcf of both 672 and 864

672 = 2 × 2 × 2× 2× 2 × 3 ×7

864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

hcf = 2 × 2 × 2× 2× 2 × 3

hcf = 96

so 96 is the largest two digit number