Question

In the following exercises, find the greatest common factor.

$10p^{3}q,12p{q}^2$

Short answer

GCF is$2pq$.

Step-by-step solution

Step 1. Given information.

The given expressions are:

$10p^{3}q\mathrm{and}12p{q}^2$

Step 2. Find the GCF.

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

$$\begin{gathered} 10p^{3}q=2·5·p·p·p·q \\ 12p{q}^2=2·2·3·p·q·q \end{gathered}$$

Bring down the common factors,

GCF is:

$$\begin{gathered} =2·p·q \\ =2pq \end{gathered}$$