Question

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

Answer 1

By Euclid's division algorithm

$963=657\times 1+306$

$657=306\times 2+45$

$306=45\times 6+36$

$45=36\times 1+9$

$36=9\times 4+0$

Since the reminder becomes here so HCF of 657 and 963 is 9 Now

$657x+963\times (-15)=HCF$ of these number

$657x+963x(-15)=9$

$657x=14454$

$x=22$