###### Example 7.1.2 Finding the Greatest Common Factor

What is the common factor between \(6x^2\) and \(70x\text{?}\) Break down each of these into its factors:

\begin{align*}
6x^2 \amp =2\cdot3\cdot x\cdot x \amp 70x \amp =2\cdot5\cdot7\cdot x\\
\end{align*}

And identify the common factors:

\begin{align*} 6x^2 \amp =\attention{2}\cdot3\cdot \attention{x}\cdot x \amp 70x \amp =\attention{2}\cdot5\cdot7\cdot \attention{x} \end{align*}With \(2\) and \(x\) in common, the greatest common factor is \(2x\text{.}\)