Question

if hcf of 78 and 143 is expressible in the form 78m -143, then find the value of m.

Answer 1

Prime factors of 78 = 2 × 3 × 13
prime factors of 143 = 11 × 13

HCF of {78, 143} = Hight common factor of {78, 143} = 13
now, 13 = 78m - 143
⇒ 13 = 78m - 143
⇒ 143 + 13 = 78m
⇒ 156 = 78m
⇒m = 156/78 = 2

Hence, answer is m = 2