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`

Step-by-step 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) * {x}^(2) * y`


and



`5 {x}^(4) {y}^(2) = 5 * {x}^(4) * {y}^(2)`


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



`= {x}^(2) y`