Question

If x and y are positive integers such that the greatest common factor of x^2y^2 and xy^3 is 45, then which of the following could y equal?

Answer 1

No answers were provided from which to select;
the only possible answers are `y=1` or `y=3`

Explanation:

`x^2y^2` and `xy^3` have a common factor of `xy^2`

If `x` and `y` are positive integers any common factor of `x^2y^2` and `xy^3` must itself have a factor of `y^2`

If `45` is the greatest common factor (or any factor) of `x^2y^2` and `xy^3`
then `45` must contain `y^2` as a factor.

Restricting ourselves to positive factors:
`color(white)("XXX")45=1^2xx3^2xx5`

So `y` must be either `1` or `3`