Question

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

Answer 1

`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`.