Question

Use Euclid's division algorithm to find the HCF of:
(i) $135$ and $225$ (ii) $196$ and $38220$ (iii) $867$ and $255$.

Find the highest HCF among them.

Answer 1

(i) By Euclid's division lemma,

$225=135\times 1+90$

$r=90\ne 0$

$135=90\times 1+45$

$r=45\ne 0$

$90=45\times 2+0$

$r=0$

So,H.C.F of $135$ and $225$ is $45$

(ii) By Euclid's division lemma,

$38220=196\times 195+0$

$r=0$

So, H.C.F of $38220$ and $196$ is $196$

(iii) By Euclid's division lemma,

$867=255\times 3+102$

$r=102\ne 0$

$255=102\times 2+51$

$r=51\ne 0$

$102=51\times 2+0$

$r=0$

So, H.C.F of $867$ and $255$ is $51$

The highest HCF among the three is $196$.