Question

If the HCF of $65$ and $117$ is expressible in the form $65\mathrm{m}-117$, then the value of $\mathrm{m}$ is

• A. $4$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is B

$2$

Step 1: Explanation for correct option.

For option (B): $2$

As, $65=5\times 13$

And $117=9\times 13$

So, HCF of $65$ and $117$is $13$

Now according to the given condition,

$65\mathrm{m}-117=13$

$\Rightarrow$ $65\mathrm{m}=117+13$

$\Rightarrow$ $65\mathrm{m}=130$

$\Rightarrow$ $\mathrm{m}=2$

So option (B) is correct

Step 2: Explanation for incorrect option.

For option (A): $4$

If $\mathrm{m}=4$, then HCF $=65\left(4\right)-117$

$=260-117$

$=143$, which is not equals to $13$

So option (A) is incorrect

For option (C): $1$

If $\mathrm{m}=1$, then HCF $=65\left(1\right)-117$

$=-52$, which is not equals to $13$

So option (C) is incorrect

For option (D): $3$

If $\mathrm{m}=3$, then HCF $=65\left(3\right)-117$

$=195-117$

$=78$, which is not equals to $13$

So option (D) is incorrect

Hence, the correct option is (B).