# How do you find the prime factorization of 20?

Apr 8, 2016

$20 = 2 \times 2 \times 5$

#### Explanation:

You can separate out each prime factor in turn as follows:

$20$ is divisible by $2$ (i.e. even) since its last digit is even.

So divide by $\textcolor{b l u e}{2}$ to get $10$.

$10$ is divisible by $2$ since its last digit is even.

So divide by $\textcolor{b l u e}{2}$ to get $5$.

$\textcolor{b l u e}{5}$ is prime.

So we can stop and write down $20$ as the product of the primes we have found:

$20 = 2 \times 2 \times 5$

This can be written as a factor tree:

$\textcolor{w h i t e}{00000} 20$
$\textcolor{w h i t e}{0000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{000} \textcolor{b l u e}{2} \textcolor{w h i t e}{000} 10$
$\textcolor{w h i t e}{000000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{00000} \textcolor{b l u e}{2} \textcolor{w h i t e}{0000} \textcolor{b l u e}{5}$