---
tags:
  - prealgebra
  - theorems
---

> Every integer greater than one is either a prime number itself or is product
> of a unique combination of primes.

This is also known as the **Unique Factorisation Theorem**.

'Unique' means that there is not more than one way to derive the whole number.
Once you reduce the factorisation to primes, there can only be one set of
numbers that results in the target number.

For example, $24$ has the following factors: ${12, 24}$ and $6, 4$ but these are
composite numbers. The unique factorisation combination for 24 is $2, 2, 3$.
