Question

Using Euclid's division algorithm, find the HCF of 135 and 225.

• A. 65
• B. 55
• C. 45
• D. 25

Answer 1

The correct option is C 45

Apply Euclid's division lemma to given numbers $c$ and $d$ to find whole numbers $q$ and $r$ such that,

$c=dq+r,0\le r<d$

Here, $c=225,d=135$

$225=135\times 1+90$

The remainder is not equal to 0. Therefore, we apply the same process again on 135 and 90.

$135=90\times 1+45$

The remainder is not equal to 0 again. Therefore, we apply same process again on 90 and 45.

$90=45\times 2+0$

Here, The remainder is equal to 0.

Therefore, HCF of 135 and 225 is 45.