# Unique prime factorization of integers

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Unique prime factorization of integers](https://ocme.evemisslab.com/en/atlas/atlas-unique-prime-factorization/)

Every positive integer n>1 has a prime factorization whose prime multiset is unique up to factor order.

atlas-unique-prime-factorization · canonical_mko

[Unique prime factorization of integers](https://ocme.evemisslab.com/en/mko/mko-unique-prime-factorization/)

## Prerequisite nodes


- [Prime natural number](https://ocme.evemisslab.com/en/atlas/atlas-prime-number/)
- [Natural-number divisibility](https://ocme.evemisslab.com/en/atlas/atlas-natural-divisibility/)
- [Mathematical induction](https://ocme.evemisslab.com/en/atlas/atlas-mathematical-induction/)
- [Euclidean algorithm](https://ocme.evemisslab.com/en/atlas/atlas-euclidean-algorithm/)
- [Greatest common divisor and coprimality](https://ocme.evemisslab.com/en/atlas/atlas-gcd-coprime/)