If x and y are positive integers such that the greatest common factor

If x and y are positive integers such that the greatest common factor of x²y² and xy³ is 45, then which of the following could y equal?

1. 45
2. 15
3. 9
4. 5
5. 3

Answer

The correct answer is E.

The greatest common factor of x²y² and xy³ is xy², which equals 45.

Because x and y are both positive integers and 45 = 3²5, there are two possibilities for x, 5 or 45.

If x is 45, then y is 1. If x is 5, then y = 3. Thus, 3 is the answer choice.