Question

If the HCF of $408$ and $1032$ is expressible in the form $1032m-408x5$. Find $m$.

Answer 1

Step $1$ : Find the HCF of $408$ and $1032$ using Euclid's division algorithm

Using Euclid’s division algorithm,

$\begin{array}{rcl}1032& =& 408\times 2+216,\\ 408& =& 216\times 1+192,\\ 216& =& 192\times 1+24,\\ and192& =& 24\times 8+0\end{array}$

Since the remainder has come to zero so the HCF of given numbers is $24$.

Step $2$ : Find the required value:

Given that HCF is expressed as following

$$\begin{gathered} 1032m-408\times 5=24 \\ \Rightarrow 1032m=24+2040 \\ \Rightarrow m=\frac{2064}{1032} \\ \Rightarrow m=2 \end{gathered}$$

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