eolas/Mathematics/Prealgebra/Fundamental_Theorem_of_Arithmetic.md

---
categories:
  - Mathematics
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 $2, 2, 3$.
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`
Reindexing 2022-09-06 13:26:44 +01:00			`categories:`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`- Mathematics`
Reindexing 2022-09-06 13:26:44 +01:00			`tags:`
			`- prealgebra`
			`- theorems`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`

Reindexing 2022-09-06 13:26:44 +01:00			`> Every integer greater than one is either a prime number itself or is product of a unique combination of primes.`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00
			`This is also known as the Unique Factorisation Theorem.`

Reindexing 2022-09-06 13:26:44 +01:00			`'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.`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00
			`For example, $24$ has the following factors: ${12, 24}$ and $6, 4$ but these are composite numbers. The unique factorisation combination for 24 is $2, 2, 3$.`