Question

if hcf of 65 and 117 is expressible as 65m-117,then the value of m is

Answer 1

 find the HCF of 65 and 117,

117 = 1×65 + 52

65 = 1× 52 + 13

52 = 4 ×13 + 0

∴ HCF of 65 and 117 is 13.

65m - 117 = 13

65m = 117+13 = 130

∴m =130/65 = 2

Answer 2

Given: HCF of 65 and 117 is expressible as 65m - 117

To find: Value of m

Solution: Finding HCF of 65 and 117 using Prime factorization method,

The given numbers can be expressed as:

65 = 5 × 13

117 = 3 × 3 × 13

The only common prime factor of 65 and 117 is 13.

So, HCF of 65 and 117 is 13.

Now, given that HCF of 65 and 117 = 65m - 117

⇒ 13 = 65m - 117

⇒ 65m = 13 + 117 = 130

⇒ m = $\frac{130}{65} = 2$

Hence, the value of m is 2.