Question

Find g.c.d of (i) $135$ and $225$ (ii) $38220$ and $196$ by Euclid's algorithm.

Answer 1

By division algorithm

$225=135\left(1\right)+90135=90\left(1\right)+4590=45\left(2\right)+0$

$gcd(135,225)=45$

As we know $38220>196$

We know $a=bq+r0\le r\le b$

$38220=196\times 195+0$

So, $196$ is gcd.

Hence, this is the answer.