If the HCF of 65 and 117 is expressible in the form 65m -117, then the value of m is

Question

Philoid · Accepted Answer

According to Euclid’s division algorithm,

b = a × q + r, 0 ≤ r < a [using, dividend = divisor × quotient + remainder]

⇒ 117 = 65 × 1 + 52

⇒ 65 = 52 × 1 + 13

⇒ 52 = 13 × 4 + 0

∴ HCF (65, 117) = 13 (i)

Also given that, HCF (65, 117) = 65 m – 117

⇒ 65 m – 117 = 13 [from (i)]

⇒ 65 m = 130

⇒ m = 2