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

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

`18 :rarr 9 and 2`

`18 = 9 xx 2`

`9` breaks down further into `3 and 3`

`9: rarr 3xx3`

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

`18 = 2xx3xx3`

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*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*9`

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

`18=2*3*3`

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

`18=2*3*3`

The product of 2 numbers `3` can be written as a power: `3*3=3^2`, so the final answer can be written as:

`18=2*3^2`

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

`18-:color(red)2=9`

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

`9-:color(red)3=color(red)3`

This is as far as you can go.

`18=color(red)2xxcolor(red)3xxcolor(red)3`