Question

if the HCF of 65 and 117 is expressible in the form of 65m -117, then find the 'm'

Answer 1

65= 5×13
117=3×3×13

So, HCF(65, 117)= 13

Now, according to question,
HCF(65, 117) = 65m-117
13 = 65m-117
13+ 117 = 65m
130 = 65m
130/65 = m
2 = m

So, m = 2

Hope it helps!

Answer 2

65 = 5× 13
117 = 13 × 3× 3

HCF of 65 and 117 is 13

65m - 117 = 13
65m = 130
m = 2