Question

What is the greatest common factor of 9x^{2}y9x 2 y and 5x^{4}y^{2}5x 4 y 2 ?

Answer 1

ANSWER

The greatest common factor is
${x}^{2} y$

EXPLANATION

We want to find the greatest common factor of

$9 {x}^{2} y$

and

$5 {x}^{4} {y}^{2}$

The prime factorizations are;


$9 {x}^{2} y = {3}^{2} \times {x}^{2} \times y$


and


$5 {x}^{4} {y}^{2} = 5 \times {x}^{4} \times {y}^{2}$


The product of the least powers of the common factors is the greatest common factor.


$= {x}^{2} y$