# How do you find the gcf of 6x^2 + 12x + 18y^2?

Jun 24, 2015

gcf $= 6 x$

#### Explanation:

Prime factors of
$6 {x}^{2} = \left\{\textcolor{red}{2} , \textcolor{red}{3} , \textcolor{red}{x} , x\right\}$
$12 x = \left\{\textcolor{red}{2} , 2 , \textcolor{red}{3} , \textcolor{red}{x}\right\}$
$18 {x}^{2} = \left\{\textcolor{red}{2} , \textcolor{red}{3} , 3 , \textcolor{red}{x} , x\right\}$

Factors that occur in all 3 terms:
$\left\{\textcolor{red}{2 , 3 , x}\right\}$

gcf (Greatest Common Factor):
$= 2 \times 3 \times x = 6 x$