How do you find the GCF of 12qr, 8r^2, 16rt?

Jul 12, 2017

See a solution process below:

Explanation:

First, factor each individual term:

$12 q r = 2 \times 2 \times 3 \times q \times r$

$8 {r}^{2} = 2 \times 2 \times 2 \times r \times r$

$16 r t = 2 \times 2 \times 2 \times 2 \times r \times t$

Next, identify the common terms in each:

$12 q r = \textcolor{red}{2} \times \textcolor{red}{2} \times 3 \times q \times \textcolor{red}{r}$

$8 {r}^{2} = \textcolor{red}{2} \times \textcolor{red}{2} \times 2 \times \textcolor{red}{r} \times r$

$16 r t = \textcolor{red}{2} \times \textcolor{red}{2} \times 2 \times 2 \times \textcolor{red}{r} \times t$

Combine these common factors by multiplying:

$\textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{r} = 4 r$

The GCF of the three terms is $\textcolor{red}{4 r}$