---
tags:
  - Mathematics
  - Prealgebra
  - factors primes
---

### 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](../../img/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](../../img/Untitled%20Diagram-Page-3.drawio%201.png)

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