Factor Generator

What this generator does

Produces a number together with its factors — the whole numbers that divide it exactly. Aimed at factor and multiple work in maths lessons, where the answer is as useful as the question.

How to use this tool

1. Press generate for a number and its factors.

Worked examples

Example shape

24 → 1, 2, 3, 4, 6, 8, 12, 24

Common use cases

• Factors and multiples practice
• Prime-factorisation lead-in exercises
• Quick number-theory reference

How this generator works

A number is drawn and every one of its divisors is found by trial division up to its square root, pairing each divisor with its partner. Stopping at the square root is not an optimisation detail so much as the structure of the problem: divisors come in pairs that multiply to the number, and one of each pair is always at or below the root.

Limitations and good to know

• The factors listed are the whole divisors, not the prime factorisation — 12 lists 1, 2, 3, 4, 6 and 12, whose prime form is 2² × 3.
• A prime number has exactly two factors, so a prime draw produces a very short list. That is the correct answer, not a fault.
• Numbers are kept small enough that trial division is instant; factoring large numbers is genuinely hard and is what a good deal of cryptography rests on.