# How do you find the greatest common factor for the list of terms 70x^2, 30x^6, 60x^9?

Feb 12, 2017

See the entire solution process below:

#### Explanation:

To find the Greatest Common Factor of these three terms we must first factor each term separately:

$70 {x}^{2} = 2 \times 5 \times 7 \times x \times x$

$30 {x}^{6} = 2 \times 5 \times 3 \times x \times x \times x \times x \times x \times x$

$90 {x}^{9} = 2 \times 5 \times 3 \times 3 \times x \times x \times x \times x \times x \times x \times x \times x \times x$

The Common Factors are:

$70 {x}^{2} = \textcolor{red}{2 \times 5} \times 7 \times \textcolor{red}{x \times x}$

$30 {x}^{6} = \textcolor{red}{2 \times 5} \times 3 \times \textcolor{red}{x \times x} \times x \times x \times x \times x$

$90 {x}^{9} = \textcolor{red}{2 \times 5} \times 3 \times 3 \times \textcolor{red}{x \times x} \times x \times x \times x \times x \times x \times x \times x$

Therefore the GCG (Greatest Common Factor) is:

$\textcolor{red}{2 \times 5 \times} \textcolor{red}{x \times x} = 10 {x}^{2}$