How do you find the gcf of #10xy^2 + 5x^2y - 20x^3y#?

1 Answer
Jun 23, 2015

Answer:

You can factor each individual term then identify which factors occur in all terms and with what multiplicity. Then multiply those common factors together.

In your example the gcf is #5xy#

Explanation:

#10xy^2=2*5*x*y*y#

#5x^2y=5*x*y*y#

#20x^3y=2*2*5*x*y*y*y#

For all of the three terms, the factors #5#, #x# and #y# occur once. So just multiply them together to get the gcf #5xy#.

If the first term were #10x^2y^2# then #x# would be a factor of all terms with a multiplicity of 2 and the gcf would be #5x^2y#