Q. 337 - Intermediate Algebra

Question

In the following exercises, find the greatest common factor.

$12a^2{b}^3,15a{b}^2$

Step-by-Step Solution

Answer

The greatest common factor is $3a{b}^2$.

Step 1. Given information.

Consider the given expressions,

$12a^2{b}^3,15a{b}^2$

Write the expressions in factor form,

$$\begin{gathered} 12a^2{b}^3=2\times 2\times 3\times a\times a\times b\times b\times b \\ 15a{b}^2=3\times 5\times a\times b\times b \end{gathered}$$

Step 2. Take out the common factors.

Multiply the common factors,

$$\begin{gathered} =3\times a\times b\times b \\ =3a{b}^2 \end{gathered}$$