# How do you write 18 as a product of prime factors?

Sep 22, 2016

$18 = 2 \times 3 \times 3$

#### Explanation:

We take 18 and break it down into factors until we reach numbers that are primes.

$18 : \rightarrow 9 \mathmr{and} 2$

$18 = 9 \times 2$

$9$ breaks down further into $3 \mathmr{and} 3$

$9 : \rightarrow 3 \times 3$

The prime factors are multiplied together to get a product at the end and together make the answer.

$18 = 2 \times 3 \times 3$

Jan 18, 2018

See explanation.

#### Explanation:

To write a prime decomposition of a number $x$ you follow this procedure:

1. Find the lowest prime number $p$ which divides $x$. Write $x$ as a product: $x = p \cdot {x}_{1}$
2. Repeat this procedure until ${x}_{1}$ is a prime number.
3. In the final step you can write the product(s) of repeating prime numbers as a power(s).

Here we have:

$x = 18$

It is an even number, so we can write that: $18 = 2 \cdot 9$

$9$ is a compound number; it is divisible by a prime number $3$:

$18 = 2 \cdot 3 \cdot 3$

Now all the numbers are prime, so the decomposition is complete:

## $18 = 2 \cdot 3 \cdot 3$

The product of 2 numbers $3$ can be written as a power: $3 \cdot 3 = {3}^{2}$, so the final answer can be written as:

## $18 = 2 \cdot {3}^{2}$

Jan 20, 2018

$18 = 2 \times 3 \times 3$

#### Explanation:

Divide $18$ by the prime number $2$.

$18 \div \textcolor{red}{2} = 9$

Divide $9$ by the prime number $3$.

$9 \div \textcolor{red}{3} = \textcolor{red}{3}$

This is as far as you can go.

$18 = \textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{3}$