Question

A rectangular surface has length $4661$ and breadth $3318$ meters. On which the square tiles are to be put. Find the maximum length of such tiles.

Answer 1

Given length and breadth are $4661m$ and $3318m$ respectively.

Here, $4661>3318$

So, we divide $4661$ by $3318$.

By using Euclid's division lemma, we get

$4661=3318\ast 1+1343$

Here, $r=1343\ne 0$

On taking $3318$ as dividend and $1343$ as the divisor and we apply Euclid's division lemma, we get

$3318=1343\ast 2+632$

Here, $r=632\ne 0$

So, on taking $1343$ as dividend and $632$ as the divisor and again we apply Euclid's division lemma, we get

$1343=632\ast 2+79$

Here, $r=79\ne 0$

So, on taking $632$ as dividend and $79$ as the divisor and again we apply Euclid's division lemma, we get

$632=79\ast 8+0$

The remainder has now become $0$, so our procedure stops.

Since the divisor at this last stage is $79$, the HCF of $3318$ and $4661$ is $79$.