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
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, $m=2$.
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