Prime Numbers Worksheets Generator

Create Printable Prime Numbers Worksheets for Identification and Factorisation

Generate free printable prime numbers worksheets that cover three distinct skills: identifying whether a number is prime, writing the prime factorisation of a composite, and listing all primes in a given range.

The generator produces A4 or US Letter PDFs with a matching answer key, so parents and teachers can mark quickly. Every refresh picks fresh questions within the range you choose.

This is a focused tool for Year 5–Year 8 and US Grades 5–7 learners meeting primes, composites and factor trees for the first time.

Why use this prime numbers generator?

Primes sit at the heart of the secondary-school number-theory curriculum and lead directly into HCF, LCM and surd work. Regular practice builds fluency. Use it for:

• introducing primes and composites
• fluency with prime factorisation and factor trees
• KS2 SATs preparation for prime-number questions
• Year 7–8 number-theory starters
• tutor work on number sense

What you can customise

• Mode: Identify, Factorise, or Range list
• Maximum number (caps the numbers used in questions)
• Number of problems
• Answer key on or off
• Paper size: A4 or US Letter

Notes and limitations

• Identify mode asks "Is N prime?" — learners answer Yes or No.
• Factorise mode asks for the full prime factorisation in index form or a simple product.
• Range list mode asks the learner to write out every prime between two values.
• The worksheet does not print a primes-to-100 cheat sheet; the workspace is reserved for the learner's working.
• Random mode means two exports at the same settings differ.

Who these worksheets are for

Parents

Support homework on primes and composites with fresh questions that match the school textbook's range.

Teachers

Print starter tasks, revision sheets, and homework for introducing primes and factor trees.

Homeschool families

Explore number theory informally with short, printable drills.

Tutors

Diagnose whether a learner's confusion is about recognising primes, dividing them out, or expressing the answer.

Worksheet style options

Identify mode

Each question shows a single number; the learner circles "prime" or "composite". Ideal for building primality recognition.

Factorise mode

Each composite number is presented with space for a factor tree or a linear working. The answer key shows the prime factorisation.

Range list mode

The worksheet gives a pair of bounds such as "List all primes between 20 and 60" and expects the learner to write them out in order.

How to use the tool

1. Choose a mode.
2. Set the maximum number.
3. Pick how many problems you want.
4. Keep the answer key on for marking support.
5. Choose A4 or US Letter.
6. Click Generate Worksheet.
7. Preview, then download the PDF.

Worked example

With mode Factorise and a max of 100, the generator might give Factorise 84. The learner builds the factor tree 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7, giving the final answer 2² × 3 × 7. The answer key prints the same factorisation for quick marking. With mode Range list the prompt might be List all primes from 1 to 50; the answer key gives 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

Methodology

A sieve of Eratosthenes up to the chosen maximum pre-computes every prime in range. In Identify mode, questions sample roughly evenly from primes and composites. In Factorise mode, a composite is picked and its canonical prime factorisation is stored alongside it. In Range list mode, a window within the maximum is chosen and the primes inside it are extracted from the sieve. The answer key uses the same sieve data, so the marked page is always consistent with the blank.

Helpful preset ideas

• Max 50, Identify mode — first lesson on primes
• Max 100, Factorise mode — Year 6 / Grade 6 factor-tree practice
• Max 200, Range list mode — Key Stage 3 consolidation
• Answer key on for fast marking

Best ways to practise prime numbers

• Learn the primes up to 20 by heart — 2, 3, 5, 7, 11, 13, 17, 19.
• Use divisibility tests for 2, 3, 5 and 11 to speed up identification.
• When factorising, always start with the smallest prime and work upwards.
• Keep a personal primes-to-100 list for reference outside the worksheet.

Designed for A4 and US Letter Printing

Prime-number worksheets print cleanly on both A4 and US Letter. Factor-tree workings often need the full page, so print at 100% scale to avoid shrinking the working space.

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