Question

If the HCF of $657$ and $963$ is expressible in the form $657x+963x-15$find $x$.

Answer 1

Step $1$ : Find the HCF of $657$ and $963$.

Using Euclid’s division algorithm,

$$\begin{gathered} 963=657\times 1+306 \\ \Rightarrow 657=306\times 2+45 \\ \Rightarrow 306=45\times 6+36 \\ \Rightarrow 45=36\times 1+9 \\ \Rightarrow 36=9\times 4+0 \end{gathered}$$

Since the remainder has come to zero so the HCF of given numbers is $9$.

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

Given that the H.C.F. is expressed as following

$$\begin{gathered} 657x+963x-15=9 \\ \Rightarrow 1620x=24 \\ \Rightarrow x=\frac{24}{1620} \\ \Rightarrow x=\frac{2}{135} \end{gathered}$$

Hence, the value of $x$ is $\frac{2}{135}$.