Answer:
Option E.
Step-by-step explanation:
The given expressions are [tex]x^2y^2[/tex] and [tex]xy^3[/tex].
[tex]x^2y^2=x\times x\times y\times y[/tex]
[tex]xy^3=x\times y\times y\times y[/tex]
Greatest common factor of [tex]x^2y^2[/tex] and [tex]xy^3[/tex] is
[tex]GCF=x\times y\times y=xy^2[/tex]
It is given that the greatest common factor of [tex]x^2y^2[/tex] and [tex]xy^3[/tex] is 45.
[tex]xy^2=45[/tex]
[tex]x=\dfrac{45}{y^2}[/tex]
x and y are positive integers.
For y=45,15,9,5 [tex]x=\dfrac{45}{y^2}\notin Z^+[/tex]
Only for y=3,
[tex]x=\dfrac{45}{3^2}[/tex]
[tex]x=\dfrac{45}{9}[/tex]
[tex]x=5 \in Z^+[/tex]
The possible value of y is 3.
Therefore, the correct option is E.
