Prime Factorisation Question Generator

Builds a sheet of prime-factorisation questions at the level you ask for. Each number is assembled from its factors rather than drawn and then tested, so every question has a factorisation worth doing. Every question is computed and checked directly — not a fabricated or AI-guessed fact.

How many questions

Between 1 and 30. Ten fills a page.

Level

Seed (optional)

A word reproduces the same sheet, so a whole class can be given the identical set.

Gentle uses two or three factors from 2, 3 and 5. Standard adds 7 and 11 and a fourth factor; stretch goes up to 23 and six factors.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

Room to answer in

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. The page addresses and dates a browser normally prints across the top and bottom are already kept off.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

Your questions will appear here.

What this generator does

Generates prime factorisation questions with answers in index form. Numbers are chosen to have interesting factorisations rather than at random — a number that turns out to be prime, or is just two times something, does not exercise the method.

How to use this tool

Choose a level and how many questions you want.
Press make questions and work through the sheet.
Show the answers to mark it, or show the working to see the division ladder each answer comes from.
Enter a seed word to rebuild the same sheet later.

Common use cases

Prime-factorisation practice
Quick maths warm-ups
Self-testing before a maths quiz

Randomness and fairness

The prime factors are drawn first with the browser's cryptographic random number generator and multiplied together to make the question. Building the number from its factors guarantees a factorisation worth doing, which drawing a number at random does not — a number picked at random is prime or nearly prime far too often. A seed word rebuilds the same sheet later; it is for reproducibility, not cryptographic strength, so a seeded sheet is deterministic rather than unpredictable.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

Factors come from the primes up to 23, so no question needs a prime you would have to hunt for.
Answers are in index form. A list with the repeats written out is the same factorisation and is not marked wrong here, but the sheet shows the index form because that is what is asked for.
Highest common factor and lowest common multiple are the usual next step and are not asked here, though the factorisations are exactly what you would need for them.

Common mistakes

Stopping before every factor is prime: 12 = 3 × 4 is not finished, because 4 is not prime. Keep splitting until every branch ends in a prime.
Forgetting that 1 is not prime: It has only one factor, not two, so it never appears in a prime factorisation.