Q. 3 - Intermediate Algebra

Question

In the following exercises, find the greatest common factor.  

$12m^2{n}^3,30m^5{n}^3$

Step-by-Step Solution

Answer

The GCF of the given expressions is $6m^2{n}^3$.

Step 1. Given Information

The given expressions are $12m^2{n}^3,30m^5{n}^3$.

Step 2. Factoring

• Factor each of the given expressions.

$$\begin{gathered} 12m^2{n}^3=2·2·3·m·m·n·n·n \\ 30m^5{n}^3=2·3·5·m·m·m·m·m·n·n·n \end{gathered}$$

• From the factors of the given expression, it is observed that the common factors are $2,3,m,m,n,n,n$.
• Multiply the common factors to determine the GCF of the given expressions.

$2·3·m·m·n·n·n=6m^2{n}^3$

• So, the GCF of the given expressions is $6m^2{n}^3$.