Question

If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is 4.

• A. True
• B. False

Answer 1

The correct option is B False

By Euclid's division algorithm
b = aq+r, 0≤r⇒ 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 …..(ii)
From the eq (i) and (ii), we get
65m - 117 = 13
65m = 130
m = 2

Hence, the given statement is false.