# How do you write 30 + 54 as the sum of two numbers times their GCF?

Oct 10, 2017

See a solution process below:

#### Explanation:

Find the prime factors for each number as:

$30 = 2 \times 3 \times 5$

$54 = 2 \times 3 \times 3 \times 3$

Now identify the common factors and determine the GCF:

$30 = \textcolor{red}{2} \times \textcolor{red}{3} \times 5$

$54 = \textcolor{red}{2} \times \textcolor{red}{3} \times 3 \times 3$

Therefore:

$\text{GCF} = \textcolor{red}{2} \times \textcolor{red}{3} = 6$

Now, we can factor $\textcolor{red}{6}$ from each number giving:

$\left(\textcolor{red}{6} \times 5\right) + \left(\textcolor{red}{6} \times 9\right) \implies$

$\textcolor{red}{6} \left(5 + 9\right)$

Oct 10, 2017

$84 = 6 \times \left(7 + 7\right)$
Or, completely written out:
$30 + 54 = 6 \times \left(7 + 7\right)$

#### Explanation:

First, we find their Greatest Common Factor:
$30 = 2 \times 3 \times 5$
$54 = 2 \times 3 \times 3 \times 3$
$G C F = 6$

The sum of the two numbers is $30 + 54 = 84$
Divide by the GCF to get a multiplicative factor easily:

$\frac{84}{6} = 14$ We convert $14$ into a simple sum:
$14 = 7 + 7$ and then combine them into the final expression.
$84 = 6 \times \left(7 + 7\right)$