Question

If HCF (51, 85) = 2 m - 1, then find m.​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

The given numbers are 51 and 85

• Prime factorization of 51 = 17 × 3

• Prime factorization of 85 = 17 × 5

So,

• It implies,

$\sf \: HCF (51, 85) = \: 17$

Now,

According to statement,

$\sf \: HCF (51, 85) = \: 2m \: - \: 1$

So,

• It implies,

$\rm :\implies\:2m - 1 = 17$

$\rm :\implies\:2m = 17 + 1$

$\rm :\implies\:2m = 18$

$\boxed{ \pink{\rm :\implies\:m \: = \: 9}}$