Question

In the following exercises, find the greatest common factor.

$30x^2,18x^3$

Short answer

GCF is $6x^2$.

Step-by-step solution

Step 1. Given information.

The given expressions are:

$30x^2,18x^3$

Step 2. Find the GCF.

Factor each coefficient into primes and write the variables with exponents in expanded form.

$$\begin{gathered} 30x^2=2·3·5·x·x \\ 18x^3=2·3·3·x·x·x \end{gathered}$$

Bring down the common factors,

GCF is:

$$\begin{gathered} =2·3·x·x \\ =6x^2 \end{gathered}$$