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. The sheet below shows how many pages they take.

Level

Seed (optional)

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

Gentle multiplies two to four primes from 2, 3, 5 and 7. Standard uses three to five, adding 11 and 13; stretch uses four to six, up to 23. No number goes above 20,000, so a draw of large primes stops early with fewer 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 built to have a factorisation worth doing rather than drawn at random — a number that turns out to be prime 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 full list of prime factors before the repeats are collected.
Enter a seed word to rebuild the same sheet later.

Worked examples

Gentle level, seed round9: 60 → 2² × 3 × 5, with the working listing 60 = 2 × 2 × 3 × 5 before the repeats are collected into indices.

Common use cases

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

How this generator works

A small handful of primes up to 23 are drawn and multiplied together to make the target number, so the answer is known before the question is set rather than discovered by factorising afterwards. The working states the method — divide by the smallest prime that goes in, and keep going with the result — then gives the full list of prime factors and collects the repeats into indices; it does not print each intermediate quotient. The index-form answer is checked by multiplying the primes back out and confirming the product matches the original number.

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 unless the generator has changed since; the seed 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; the HCF and LCM question generator sets those, and these factorisations are exactly what they need.

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.