# How do you rewrite 35 + 20 using the GCF and a sum of two numbers?

Nov 1, 2017

See a solution process below:

#### Explanation:

First, find the prime factors for each number as:

$35 = 5 \times 7$

$20 = 2 \times 2 \times 5$

Now identify the common factors and determine the GCF:

$35 = \textcolor{red}{5} \times 7$

$20 = 2 \times 2 \times \textcolor{red}{5}$

Therefore:

$\text{GCF} = \textcolor{red}{5}$

We can now write the expression as:

$\left(\textcolor{red}{5} \times 7\right) + \left(\textcolor{red}{5} \times 4\right) \implies$

$\textcolor{red}{5} \left(7 + 4\right)$

Nov 1, 2017

$55 = 5 \left(7 + 4\right) \to$ [ANS}

#### Explanation:

What is the greatest common factor (GCF)?
That is the largest number that will divide into all those given.
To find it, the smallest prime numbers should be divided into each one. Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19.

Looking at $20$ and $35$, we can see that the first number on the list that will divide into both is $5$.

$2$ will divide into one and $7$ will divide into the other, but only $5$ will divide into both.

So the GCF is $5$.

The Sum of $35 + 20 = 55$

And the question states that $S u m = G C F \left(a + b\right) \to \left[1\right]$

Subbing in values: $55 = 5 \left(a + b\right)$

$\cancel{55} 11 = \cancel{5} \left(a + b\right)$

$\left(a + b\right) = 11 \to$ which is the requested another sum

Factoring $5$ into each number, we get $7$ and $4$.

$S u m = G C F \left(a + b\right)$

$55 = 5 \left(7 + 4\right) \to$ [ANS]

To check:

$55 = 5 \left(7 + 4\right)$

$55 = 35 + 20$

$55 = 55$