Question

Find the HCF and LCM of $306$and $657$ by prime factorization method.

Answer 1

Step $1$: Find HCF of the given numbers

Given numbers, $306$and $657$

Prime Factorization of $306=2\times 3\times 3\times 17$

Prime Factorization of $657=3\times 3\times 73$

$\therefore$HCF $=3\times 3=9$

Step $2$: Find LCM

We know that, Product of two numbers $=$ $LCM\times HCF$

Let, the LCM be $x$.

$\Rightarrow$ H.C.F $\times x=306\times 657$

$\Rightarrow 9\times x=306\times 657$

$\Rightarrow x=\frac{306\times 657}{9}$

$\Rightarrow x=22338$

Hence, HCF and LCM are $9$ and $22338$ respectively.