Question

If the HCF of $85$and $153$ is expressible in the form of $85m-153$, the value of $m$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B

$2$

Explanation of the correct option.

Step $1$ : Find the HCF of $85$ and $153$.

Using Euclid’s division algorithm,

$$\begin{gathered} 153=85\times 2+68 \\ \Rightarrow 85=68\times 1+17 \\ \Rightarrow 68=17\times 4+0 \end{gathered}$$

Since the remainder has come to zero so the H.C.F. of given numbers is $17$.

Step $2$ : Find the value of $m$.

From given data H.C.F. is written as:

$$\begin{gathered} 85m-153=17 \\ \Rightarrow 85m=17+153 \\ \Rightarrow m=\frac{170}{85} \\ \Rightarrow m=2 \end{gathered}$$

Hence, the value of $m$ is $2$.

Hence, option $B$ is the correct answer.