Question

If two positive integers $a$ and $b$ are written as $a=x^2{y}^2$ and $b=x{y}^2$; $x$, $y$ are prime numbers then the $HCF(a,b)$ is

Answer 1

HCF by using the prime factorization method.

Step1:

$\text{Find the prime factorization of each of the number}$

Step2:

$\text{The product of all common prime factor is the HCF}$

Here,

$\Rightarrow a=x\times x\times y\times y$

$\Rightarrow b=x\times y\times y$

common Factors are $x\times y\times y$

Thus ,

$HCF(a,b)=x{y}^2$