Factors & Multiples Worksheets

Create Printable Factors & Multiples Worksheets for HCF and LCM Practice

Generate free printable factors and multiples worksheets covering the five classic skills of the topic: listing factor pairs, listing the first few multiples of a number, finding the highest common factor (HCF), finding the lowest common multiple (LCM), and mixed practice across all four.

The generator produces A4 or US Letter PDFs with a matching answer key. Every refresh creates a new mix of questions within the number range you choose.

This tool is aimed at Year 5–Year 8 and US Grades 5–7, where factor pairs, HCF and LCM appear in the curriculum as a bridge between multiplication fluency and algebra.

Why use this factors & multiples generator?

HCF and LCM are the two operations most commonly muddled: learners find the highest common factor when they were asked for the lowest common multiple, and vice versa. Concentrated, varied practice unpicks that confusion. Use it for:

• introducing factor pairs in Year 4 and Year 5
• HCF and LCM teaching in Year 6 and Key Stage 3
• fraction addition prep (LCM of denominators)
• SATs revision and middle-school number work
• tutor sessions targeting HCF / LCM mixing-up

What you can customise

• Mode: Factors, Multiples, HCF, LCM, or Mixed
• Number range (upper bound for the values used in questions)
• Number of problems
• Answer key on or off
• Paper size: A4 or US Letter

Notes and limitations

• Factors and multiples are printed as comma-separated lists.
• HCF and LCM answers are single integers.
• Ranges around 30–60 suit Year 5–6; push higher for older learners working with larger factor sets.
• Random mode means two exports with the same settings will differ.

Who these worksheets are for

Parents

Support children's homework on factors and multiples with fresh, relevant practice that matches the classroom range.

Teachers

Differentiate by setting a smaller range for some children and a larger one for others, then print multiple versions of the same worksheet.

Homeschool families

Cover the full HCF/LCM topic without buying a dedicated workbook.

Tutors

Use Mixed mode to diagnose which specific sub-skill a learner is missing.

Worksheet style options

Factors mode

Each question asks the learner to list every factor of a given number. Answers are shown as ordered comma-separated lists.

Multiples mode

Each question asks for the first few multiples of a given number (usually the first six).

HCF mode

Two numbers are given; the learner writes the highest common factor as a single integer.

LCM mode

Two numbers are given; the learner writes the lowest common multiple as a single integer.

Mixed mode

An even sampling of all four above. This is the best mode once the skills have been taught in isolation.

How to use the tool

1. Choose a mode.
2. Set the number range.
3. Pick the problem count.
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

In Factors mode with range 50, a question might be List the factors of 36. The answer is 1, 2, 3, 4, 6, 9, 12, 18, 36, written on the answer key. In HCF mode with range 40, a question might be HCF(24, 36); the answer is 12. In LCM mode, LCM(6, 8) gives 24.

Methodology

For Factors, the engine iterates from 1 to the square root of N, collecting each divisor and its pair. For Multiples, it lists n, 2n, 3n… for the required length. HCF is found by the Euclidean algorithm; LCM is derived as a × b / HCF(a, b). Every answer-key entry is computed from the same deterministic functions, so the marked page always agrees with the blank.

Helpful preset ideas

• Range 24, Factors — factor-pair warm-ups for Year 4
• Range 50, Multiples — times-table reinforcement
• Range 60, Mixed — Year 6 SATs revision
• Range 100, HCF and LCM — Key Stage 3 consolidation

Best ways to practise factors & multiples

• Write factors in pairs, working inwards from 1 × N.
• For LCM of two numbers, list multiples of the larger number first — it is almost always faster.
• Remember: HCF is never larger than the smaller input; LCM is never smaller than the larger input.
• Use prime factorisation as a backup when numbers get awkward.

Designed for A4 and US Letter Printing

Factor and multiple worksheets print cleanly on A4 and US Letter. Comma-separated answer lists benefit from full page width, so print at 100% scale.

Related maths practice tools

• Prime Numbers Worksheets Generator
• Square & Cube Numbers Generator
• Multiplication Table Generator
• Mixed Tables Generator
• Fractions Practice Sheets Generator