Q. 338 - Intermediate Algebra

Question

In the following exercises, find the greatest common factor.

$12m^2{n}^3,42m^5{n}^3$

Step-by-Step Solution

Answer

The greatest common factor is $6m^2{n}^3$.

Step 1. Given information.

The expressions are,

 $12m^2{n}^3,42m^5{n}^3$

Step 2. Finding the greatest common factor.

Now, the factored form of the given expressions is

$$\begin{gathered} 12m^2{n}^3=2\times 2\times 3\times m\times m\times n\times n\times n \\ 42m^5{n}^3=2\times 3\times 7\times m\times m\times m\times m\times m\times n\times n\times n \end{gathered}$$

Then the common factors are

$2\times 3\times m\times m\times n\times n\times n=6m^2{n}^3$

Hence, the greatest common factor is $6m^2{n}^3$.