Question

In the following exercises, find the greatest common factor.

$27p^2{q}^3,45p^3{q}^4,9p^4{q}^3$

Short answer

The GCF of the given expressions is$9p^2{q}^3$.

Step-by-step solution

Step 1. Given Information

The given expressions are$27p^2{q}^3,45p^3{q}^4,9p^4{q}^3$.

Step 2. Factoring

• Factor each of the given expressions.

$$\begin{gathered} 27p^2{q}^3=3·3·3·p·p·q·q·q \\ 45p^3{q}^4=3·3·5·p·p·p·q·q·q·q \\ 9p^4{q}^3=3·3·p·p·p·p·q·q·q \end{gathered}$$

• From the factors of the given expression, it is observed that the common factors are $3,3,p,p,q,q,q$.
• Multiply the common factors to determine the GCF of the given expressions.

$3·3·p·p·q·q·q=9p^2{q}^3$

• So, the GCF of the given expressions is $9p^2{q}^3$.