# How do you find the GCF of 12y^3 and 15y^2?

Oct 2, 2015

GCF = $3 {y}^{2}$

#### Explanation:

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The Greatest Common Factor (GCF) is the product of all the common factors:
$\textcolor{w h i t e}{\text{XXX}} 3 \times y \times y = 3 {y}^{2}$

Note:
$\textcolor{w h i t e}{\text{XXX}} 12 {y}^{3} \div 3 {y}^{2} = 4 y$
$\textcolor{w h i t e}{\text{XXX}} 15 {y}^{2} \div 3 {y}^{2} = 5$
$4 y$ and $5$ have no common factors, so $3 {y}^{2}$ is the Greatest Common Factor of $12 {y}^{3}$ and $15 {y}^{2}$