# What is the GCF of 18a^2b^2 − 6ab^2 + 12ab^3?

Jun 21, 2018

GCF is $6 a {b}^{2}$

#### Explanation:

Given: $18 {a}^{2} {b}^{2} - 6 a {b}^{2} + 12 a {b}^{3}$

The GCF is the greatest common factor. TO find it you can decompose each monomial:

$18 {a}^{2} {b}^{2} : \text{ } \textcolor{red}{2} \cdot \textcolor{red}{3} \cdot 3 \cdot \textcolor{red}{a} \cdot a \cdot \textcolor{red}{b} \cdot \textcolor{red}{b}$

$- 6 a {b}^{2} : \text{ } - 1 \cdot \textcolor{red}{2} \cdot \textcolor{red}{3} \cdot \textcolor{red}{a} \cdot \textcolor{red}{b} \cdot \textcolor{red}{b}$

$12 a {b}^{3} : \text{ } \textcolor{red}{2} \cdot 2 \cdot \textcolor{red}{3} \cdot \textcolor{red}{a} \cdot \textcolor{red}{b} \cdot \textcolor{red}{b} \cdot b$

The GCF is $6 a {b}^{2}$