# How do you find the gcf of  6a + 18a^2?

Jul 9, 2015

Prime factors:
$\textcolor{w h i t e}{\text{XXXX}}$$6 a = \textcolor{b l u e}{2} \times \textcolor{b l u e}{3} \times \textcolor{b l u e}{a}$
$\textcolor{w h i t e}{\text{XXXX}}$$18 {a}^{2} = \textcolor{b l u e}{2} \times \textcolor{b l u e}{3} \times 3 \times \textcolor{b l u e}{a} \times a$

Select pairs of identical terms from each factoring:
$\textcolor{w h i t e}{\text{XXXX}}$$2 \times 3 \times a = 6 a$

The greatest common factor (gcf) of $6 a$ and $18 {a}^{2}$ is
$\textcolor{w h i t e}{\text{XXXX}}$$6 a$.

(...and, yes, you could have simply recognized that $\left(6 a\right)$ is a factor of $\left(18 {a}^{2}\right)$ but it is probably better to see how this should be handled in the general case.)