ANSWER
The greatest common factor is
[tex] {x}^{2} y[/tex]
EXPLANATION
We want to find the greatest common factor of
[tex]9 {x}^{2} y[/tex]
and
[tex]5 {x}^{4} {y}^{2} [/tex]
The prime factorizations are;
[tex]9 {x}^{2} y = {3}^{2} \times {x}^{2} \times y[/tex]
and
[tex]5 {x}^{4} {y}^{2} = 5 \times {x}^{4} \times {y}^{2} [/tex]
The product of the least powers of the common factors is the greatest common factor.
[tex] = {x}^{2} y[/tex]
