Question

Using Euclid's algorithm, find the $\mathrm{HCF}$ of $240$ and $228$.

Answer 1

The objective is to find the $\mathrm{HCF}$ of the given numbers using Euclid's algorithm.

According to Euclid's algorithm,

$a=qb+r$

Where $a$ and $b$ are the numbers for which $\mathrm{HCF}$ needs to be calculated and $q$ and $r$ are quotient and remainder.

As $240>228$, this implies that $a=240$ and $b=228$.

$$\begin{gathered} 240=1\times 228+12 \\ 228=19\times 12+0 \end{gathered}$$

Here, the remainder in the last expression is zero.

Final answer :

Hence, the HCF for the given numbers is 12.