---
tags:
  - prealgebra
  - number-theory
---

# Prime factorisation

Prime factorisation is the activity of expressing a composite number as the
unique product of [prime numbers](Primes%20and%20composites.md). There are two
main approaches to this:

- - factor\* trees
- repeated division by two

> **Factor trees:** we take a number $n$ and break it down into two factors of
> $n$. We then repeat this process with the resulting factors working
> recursively until the numbers we are left with are primes.

![Untitled Diagram-Page-1.drawio.png](static/Untitled%20Diagram-Page-1.drawio.png) _The
prime factors of 27 are 2, 3, 3_

it doesn't matter which products we choose as the interim factors, we should
always reach the same outcome:
![Untitled Diagram-Page-3.drawio 1.png](static/Untitled%20Diagram-Page-3.drawio%201.png)

![Untitled Diagram-Page-2.drawio.png](static/Untitled%20Diagram-Page-2.drawio.png)
