Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

By Euclid’s division algorithm,
b = aq + r, 0 ≤ r < a
[∵ dividend = divisor x quotient + remainder]
⇒ 117 = 65 x 1 + 52
⇒ 65 = 52 x 1 + 13
⇒ 52 = 13 x 4 + 0
∴ HCF (65, 117) = 13 …(i)
Also, given that, HCF (65, 117)
= 65m -117 …(ii)

From (i) and (ii),
65m – 117 =13
⇒ 65m = 130
⇒ m = 2