Question

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

A) 4
B) 2
C) 1
D) 3

Answer 1

The answer is B.
By Euclid's division algorithm,
$b=aq+r,0\le r<a[\because dividend=divisor\times quotient+remainder]$
$\Rightarrow 117=65\times 1+52$
$\Rightarrow 65=52\times 1+13$
$\Rightarrow 52=13\times 4+0$
$\therefore$ HCF (65, 117) = 13
Also, given that, HCF (65, 117) = 65m - 117
65m - 117 = 13
65m = 130
m = 2