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

Answer:

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:

XXX

45  =  12  ×  32  ×  5

So  y  must be either  1  or  3