How do you find the gcf of 20x^2 - 18xy?

Jun 24, 2015

The two terms of $20 {x}^{2} - 18 x y$ have a gcf of $2 x$

Explanation:

Prime factors of:
$20 {x}^{2}$ are $\left[\textcolor{red}{2} , 2 , 5 , \textcolor{red}{x} , x\right]$
$18 x y$ are $\left[\textcolor{red}{2} , 3 , 3 , \textcolor{red}{x} , y\right]$

The factors common to both prime factor decomposition are:
$\textcolor{w h i t e}{\text{XXXX}}$$\left[2 , x\right]$
and the greatest common factor (gcf) is
$\textcolor{w h i t e}{\text{XXXX}}$$2 \times x = 2 x$