Question

In the following exercises, find the greatest common factor.

$8a^2{b}^3,10a{b}^2$

Short answer

The GCF of the given expressions is$2a{b}^2$.

Step-by-step solution

Step 1. Given Information

The given expressions are$8a^2{b}^3,10a{b}^2$.

Step 2. Factoring  

• Factor each of the given expressions.

$$\begin{gathered} 8a^2{b}^3=2·2·2·a·a·b·b·b \\ 10a{b}^2=2·5·a·b·b \end{gathered}$$

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

$2·a·b·b=2a{b}^2$

• So, the GCF of the given expressions is $2a{b}^2$.