Question

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.

Options

• 4

• 2

• 1

• 3

Answer 1

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is 2.

Explanation:

Let us find the HCF of 65 and 117,

117 = 1 × 65 + 52

65 = 1 × 52 + 13

52 = 4 × 13 + 0

Hence, we get the HCF of 65 and 117 = 13.

65m – 117 = 13

65m = 117 + 13 = 130

∴ m = `130/65` = 2