# How do you find the GCF of 24cd^3, 48c^2d?

Mar 3, 2018

See a solution process below:

#### Explanation:

First, we can write the prime factor for each term as:

$24 c {d}^{3} = 2 \times 2 \times 2 \times 3 \times c \times d \times d \times d$

$48 {c}^{2} d = 2 \times 2 \times 2 \times 2 \times 3 \times c \times c \times d$

The common prime factors are:

$24 c {d}^{3} = \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{c} \times \textcolor{red}{d} \times d \times d$

$48 {c}^{2} d = \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{2} \times 2 \times \textcolor{red}{3} \times \textcolor{red}{c} \times c \times \textcolor{red}{d}$

Therefore the Greatest Common Factor is:

$\text{GCF} = \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{c} \times \textcolor{red}{d} = 24 c d$