Definition
Prime factorisation
Prime factorisation writes a whole number greater than 1 as a product made only from prime numbers.
What it means
Break the number into factors. Keep breaking any composite factor until every factor is prime. Different correct routes finish with the same prime factors, although they may be written in a different order.
Remember it
Keep splitting until every branch ends at a prime.
Example
For 84: 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7 = 2² × 3 × 7.
Watch for
The number 1 is neither prime nor composite and does not have a prime factorisation.
Common mix-up
A factor pair such as 12 × 7 is not finished for 84 because 12 is not prime.
Exact meaning
A prime factorisation expresses a positive integer greater than 1 as a product of prime factors. Apart from the order of those factors, the factorisation is unique.