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

Eli Assouline

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

#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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Allen

( y ) could equal 15.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.