Fiducia TogetherTypes of number
Integers, primes, factors, multiples, squares, cubes and roots.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
The vocabulary of number: integers are whole numbers; primes have exactly two factors; factors divide into a number; multiples are in its times table.
Where it applies
Both tiers, and it underlies HCF, LCM and prime factorisation.
How it works
Prime factorisation writes a number as a product of primes, which is how HCF and LCM are found reliably rather than by listing.
1 is not prime — it has only one factor.
How to use it in your work
Use a factor tree and write the answer in index form.
For HCF take the lowest power of each shared prime; for LCM take the highest power of every prime present.
Check whether a question wants factors or multiples. They are opposite and the words are easily misread under pressure.
Where to get help
Your teacher and your board's specification and mark scheme.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.