Question

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

Answer 1

The correct option is B

2

Explanation for the correct option:

HCF: It means the Highest Common Factor. When finding the factors of two or more numbers, some numbers are found to be common.

Step 1: Finding the HCF of $65$ and $117$:

$$\begin{gathered} 117=9\times 13 \\ 65=5\times 13 \end{gathered}$$

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

Step 2: Finding the value of $m$:

According to the question, HCF of $65$ and $117$ is expressible in form $65m-117$. Hence,

$65m-117=13$

Adding $117$to both sides of the equation.

$65m-117+117=13+117$

$65m=130$

Divide both sides by $65$.

$\boxed{m=2}$

Hence, option (b) is the correct option.