Q. 6.2 - Intermediate Algebra

Question

Find the greatest common factors: $14x^3,70x^2,105x$. 

Step-by-Step Solution

Answer

The GCF of the given expressions is $7x$. 

Step 1. Given information

The given expressions are $14x^3,70x^2,105x$.

Step 2. Factoring

• Factor each of the given expressions.

$$\begin{gathered} 14x^3=2·7·x·x·x \\ 70x^2=2·5·7·x·x \\ 105x=3·5·7·x \end{gathered}$$

• From the factors of the given expression, it is observed that the common factors are $7,x$.
• Multiply the common factors to determine the GCF of the given expressions.

$7·x=7x$

• So, the GCF of the given expressions is $7x$.