What is Prime Factorisation?
Writing a number as a product of its prime factors. Every composite number has exactly one prime factorisation (ignoring the order of factors).
A prime number is a whole number greater than 1 that has no factors other than 1 and itself (e.g. 2, 3, 5, 7, 11…). A composite number can be broken down into prime factors.
When we write a composite number as a product of prime factors, we say it is in prime factored form.
For example, the prime factorisation of 12 is:
Prime factorisation is unique — no matter which method you use, you will always arrive at the same set of prime factors for a given number.
Two Methods: Repeated Division and Factor Trees
There are two popular methods for finding the prime factorisation of a number:
- Repeated Division — Systematically divide by the smallest prime factor, then the next, and so on until you reach 1.
- Factor Tree — Split the number into any factor pair, then keep splitting each branch until every branch ends in a prime number.
Think of a factor tree like peeling an onion — each layer you peel away reveals smaller and smaller pieces, until you can't peel any further. Those innermost pieces are your prime factors.
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