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

Format

76: 1, 2, 4, 19, 38, 76 and 391: 1, 17, 23, 391 — two draws; 391 looks prime and is 17 × 23

Common use cases

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

How this generator works

A number between 10 and 500 is drawn and every whole number from 1 up to the number itself is tested as a divisor, in order, which is why the factors come out sorted. At this size the full scan is instant; the usual shortcut — testing only up to the square root and pairing each divisor with its partner — matters for large numbers and is not needed here.

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.