Question

Find the HCF using Euclids Algorithm. 136,170,255.

Answer 1

Consider the problem

Euclid division

$a=bq+r$

$0\le r<b$

First we find the HCF of $255$ and $170$

$\begin{array}{c}255=170\left(1\right)+85\\ 170=85\left(2\right)+0\end{array}$

So, HCF of $255$ and $170$ is $85$

Now, find the HCF of $136$ and $85$

$\begin{array}{c}136=85\left(1\right)+51\\ 85=51\left(1\right)+34\\ 51=34\left(1\right)+17\\ 34=17\left(2\right)+0\end{array}$

HCF of $136$ and $85$ is $17$

Therefore,

$HCF\left(136,170,255\right)=17$