Question

If the H.C.F of $657$ and $963$ is expressible in the form $657x-(963\times 15)$, find $x$.

Answer 1

Using Euclid's division
$a=bq+r$
$963=657\times 1+306$
$657=306\times 2+45$
$306=45\times 6+36$
$45=36\times 1+9$
$36=9\times 4+0$
$\therefore$H.C.F$=9$
$\therefore 9=657x-(963\times 15)$
$657x=14454$
$x=22$