If the HCF of $65$ and $117$ is expressible in the form $65m-117$ then find the value of $m$.

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

To do: 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 $13$.

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

$\therefore 65m-117=13$

$\Rightarrow 65m=13+117$

$\Rightarrow 65m=130$

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

$\Rightarrow m=2$

Thus, $m=2$.

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Updated on: 10-Oct-2022

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