Question

If the HCF of 65 and 117 is of the form (65m − 117), then m = ?

(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

(b) 2
It is given that:
HCF (65, 117 ) = ( 65m − 117)
We know,
65 = 13 $\times$ 5
117 = 13 $\times$ 9
∴ HCF = 13
∴ 65m − 117 = 13
65m = 13 + 117 = 130
$\Rightarrow$ m = $\frac{130}{65}=2$
∴ m = 2