Q. 4 - Intermediate Algebra

Question

In the following exercises, find the greatest common factor.

$28x^2{y}^4,42x^4{y}^4$

Step-by-Step Solution

Answer

The GCF of the given expressions is $14x^2{y}^4$.

Step 1. Given Information

The given expressions are $28x^2{y}^4,42x^4{y}^4$.$28x^2{y}^4,42x^4{y}^4$

Step 2. Factoring

• Factor each of the given expressions.

$$\begin{gathered} 28x^2{y}^4=2·2·7·x·x·y·y·y·y \\ 42x^4{y}^4=2·3·7·x·x·x·x·y·y·y·y \end{gathered}$$

• From the factors of the given expression, it is observed that the common factors are $2,7,x,x,y,y,y,y$.
• Multiply the common factors to determine the GCF of the given expressions.

$2·7·x·x·y·y·y·y=14x^2{y}^4$

• So, the GCF of the given expressions is $14x^2{y}^4$.