Question

Using Euclid's division algorithm prove that $847,2160$ are Co-primes relatively prime ?

Answer 1

Given, the two numbers $847,2160$

Here, Co-primes are 2 numbers which have only one as a common factor.

Let, $a=2160b=847$

Then, by Euclid's lemma

$a=bq+r,0\le r<b$

So,

$2160=847\times 2+466847=466\times 1+381466=381\times 1+85381=85\times 4+4185=41\times 2+341=3\times 13+23=2\times 1+12=1\times 2+0$

As $1$ is the $H.C.F$ of $847$ and $2160$,

$\therefore$ $847$ and $2160$ are co-primes as they have only $1$ as their $H.C.F.$