Try to think of the GCF between the coefficients and the GCF between the variables separately.
17c(3c^2-2)
Practice makes perfect
We want to find the greatest common factor — GCF — of the terms in the given expression. To do so, we will consider coefficients and variables separately.
51 c^3- 34 c
Let's start by finding the GCF of 51 and 34.
Factors of51:& 1,3, 17,and51
Factors of34:& 1,2, 17,and 34
We found that the GCF of the coefficients is 17. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
\begin{aligned}
\textbf{Factors of }\bm{1^\text{st}}\textbf{ Variable:}&\ {\color{#FF0000}{c}}, c^2, c^3\\
\textbf{Factors of }\bm{2^\text{nd}}\textbf{ Variable:}&\ {\color{#FF0000}{c}}
\end{aligned}
We see that there is one repeated variable factor, c.
Thus, the GCF of the expression is 17* c= 17c. Now we can write the given expression in terms of the GCF.
51c^3-34c ⇔ 17c* 3c^2- 17c* 2
Finally, we will factor out the GCF.
17c* 3c^2- 17c* 2 ⇔ 17c(3c^2-2)
