Question

If the $HCF$ of $65$ and $117$ can be written as $(65m-117)$, find the value of $m$.

Answer 1

Given that,

$117=1\times 65+52$

$65=1\times 52+13$

$52=1\times 12+0$

$\therefore HCF$ of $65$ and $117$ is $13$.

$65m-117=13$

$65m=117+13=130$

$\therefore$ $m=\frac{130}{65}=2$

Then,

We get the value of $m=2$