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

Dec 13, 2016

$10 {y}^{2}$

#### Explanation:

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

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.

${y}^{3} = y \cdot y \cdot y \textcolor{w h i t e}{a a a} {y}^{2} = y \cdot y$

The largest number of "$y$"'s common to both ${y}^{3}$ and ${y}^{2}$ is $y \cdot y$.

The GCF of the variables is ${y}^{2}$.

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