# How do you find the GCF of 14n, 42n^3?

Mar 7, 2018

See a solution process below:

#### Explanation:

Find the prime factors for each term as:

$14 n = 2 \times 7 \times n$

$42 {n}^{3} = 2 \times 3 \times 7 \times n \times n \times n$

Now identify the common factors and determine the GCF:

$14 n = \textcolor{red}{2} \times \textcolor{red}{7} \times \textcolor{red}{n}$

$36 = \textcolor{red}{2} \times 3 \times \textcolor{red}{7} \times \textcolor{red}{n} \times n \times n$

Therefore:

$\text{GCF} = \textcolor{red}{2} \times \textcolor{red}{7} \times \textcolor{red}{n} = 14 n$