Question

Find the HCF of the following algebraic expressions.
$5x^2{y}^2,15x^2{y}^2,3x{y}^2$

Answer 1

We first factorize the given algebraic expressions $5x^2{y}^2,15x^2{y}^2$ and $3x{y}^2$ as shown below:

$5x^2{y}^2=5\times x\times x\times y\times y15x^2{y}^2=3\times 5\times x\times x\times y\times y3x{y}^2=3\times x\times y\times y$

The common factors of $5x^2{y}^2,15x^2{y}^2$ and $3x{y}^2$ are $x$ and $y^2$, therefore, the HCF is:

$x\times y\times y=x{y}^2$

Hence, the HCF of $5x^2{y}^2,15x^2{y}^2$ and $3x{y}^2$ is $x{y}^2$.