How do you find the greatest common factor of #30y^3, 20y^2#?

1 Answer
Dec 13, 2016

Answer:

#10y^2#

Explanation:

Find the greatest common factor (GCF) of #30y^3# and #20y^2#.

First, let's find the GCF of the coefficients #30# and #20# by listing their factors.

#30#: #1, 2, 3, 5, 6, 10, 15, 30#

#20#: #1, 2, 4, 5, 10, 20#

The greatest factor that is "common" to both lists is #10#. In other words, the largest number that can "go into" both #30# and #20# without a remainder is 10.

Now, let's find the GCF of the variables.

#y^3= y *y*ycolor(white)(aaa)y^2=y*y#

The largest number of "#y#"'s common to both #y^3# and #y^2# is #y*y#.

The GCF of the variables is #y^2#.

Combing the the GCF's of the coefficients and the variables gives a GCF of #10y^2#.