# 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

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Given:

The HCF of $65$ and $117$ is expressible in the form $65m-117$.

To do:

We have to find the value of $m$.

Solution:

H.C.F. of $65$ and $117$:

$65=5\times13$

$117=3\times3\times13$

Therefore, H.C.F. of $65$ and $117$ is $13$.

HCF of $65$ and $117$ is expressible in the form $65m-117$.

Therefore,

$65m-117=13$

$\Rightarrow 65m=13+117$

$\Rightarrow 65m=130$

$\Rightarrow m=\frac{130}{2}$

$\Rightarrow m=2$

Hence, $m=2$.

Updated on 10-Oct-2022 13:27:06