Question

Find the HCF of 65 and 117 and find a pair of integral values of m and n such that HCF = 65m +
117n.

Answer 1

117 = 65 × 1 + 52

65 = 52 × 1 + 13

52 = 13 × 3 + 0

==> HCF = 13

==> 13 = 65 - 52 × 1

==> 13 = 65 - ( 117 - 65 × 1)

==> 13 = 65 - 117 + 65 × 1

==> 13 = 65 × 2 - 117 × 1

==> 13 = 65 × 2 + 117 × -1

Here,

==> HCF = 65m + 117 n

Where,

==> m = 2

==> n = -1