Question

Use Euclid's division algorithm to find the HCF of the following numbers: $55$ and $210$

Answer 1

Since $210>55$, we apply the division lemma to $210$ and $55$ to obtain:

$210=55\times 3+45$

Since remainder $45\ne 0$, we apply the division lemma to $55$ and $45$ to obtain:

$55=45\times 1+10$

Since, the remainder $10\ne 0$,we consider the new divisor $45$ and new remainder $10$, and apply the division lemma to obtain

$45=10\times 4+5$

Since remainder $5\ne 0$, now, taking the new divisor $10$ and new remainder $5$, and apply the division lemma to obtain

$10=5\times 2+0$

Since the remainder is zero, the process stops.

The divisor at last stage is $5$,

Hence, the $HCF$ of $210$ and $55$ is $5$.