Factors & Multiples Worksheets

What you can do with this worksheet generator

This tool builds printable practice sheets for four core number-theory skills: listing all factors of a number, writing the first six multiples, finding the highest common factor of two numbers, and calculating the lowest common multiple. You can generate a worksheet focused on one skill or request a mixed set that rotates through all four types. The generator produces a clean PDF ready to print on A4 or US Letter paper, with an optional second page showing worked answers.

What you can customise

• Mode: choose Factors, Multiples, HCF, LCM or Mixed to control which question types appear.
• Maximum number: set the upper limit for generated numbers, from 6 to 200 (the tool clamps multiples mode to 20 when needed to keep answers manageable).
• Problem count: request between 4 and 40 questions per sheet.
• Answer key: toggle a second page with full worked solutions.
• Name and date fields: optionally print header boxes for student details.
• Custom title: replace the default heading with your own text.

How to use the tool

1. Pick a mode from the dropdown — Factors, Multiples, HCF, LCM or Mixed.
2. Set the maximum number you want the generator to draw from (default is 60; raise it for harder worksheets or lower it for younger learners).
3. Choose how many problems to include (default is 16).
4. Tick the answer-key box if you want solutions printed on a second page.
5. Add a custom title or leave it blank to use the default heading.
6. Click Generate and download your branded PDF.

Who these worksheets are for

Teachers

Use these sheets for quick starters, homework assignments or timed drills. The mixed mode works well for end-of-unit revision, and the answer key speeds up marking.

Parents and homeschoolers

Print a fresh worksheet whenever your child needs extra practice. The adjustable number range lets you match the difficulty to their current level without hunting through textbooks.

Tutors

Generate targeted practice for weak spots — factors only for a student who struggles with prime factorisation, or HCF and LCM together to reinforce the relationship between the two concepts.

Worked classroom example

A Year 6 teacher wants a 20-question mixed worksheet for a 30-minute lesson. She selects Mixed mode, sets the maximum number to 48 (avoiding very large products), requests 20 problems and ticks the answer-key box. The generator produces a sheet with five questions of each type: list all factors of 37, list the first six multiples of 9, find HCF(24, 36), find LCM(8, 12) and so on. The answer page shows 1 and 37 for the factors question, 9, 18, 27, 36, 45, 54 for the multiples, HCF = 12 and LCM = 24. She prints thirty copies on her school printer (US Letter) and distributes them at the start of the lesson.

How it works under the hood

The engine picks random integers within your specified range, then applies the selected operation. For factors it performs trial division from 1 to n; for multiples it multiplies the base by 1 through 6; for HCF it uses Euclid's algorithm (recursive modulo); for LCM it divides the product of the two numbers by their HCF. In mixed mode the generator cycles through all four question types to guarantee a balanced spread. The layout engine arranges HCF and LCM questions in two columns and factors, multiples or mixed questions in a single column to fit the varying answer lengths.

Designed for A4 and US Letter printing

Every PDF uses a responsive margin system that fits both A4 (210 × 297 mm) and US Letter (8.5 × 11 in) paper without clipping. Print directly from your browser or save the file to print later — no scaling or page-setup tweaks required.

Notes and limitations

• The multiples mode always asks for the first six multiples; you cannot request a different count.
• When the maximum number is set above 30, LCM answers can become very large (over 500); consider clamping your range if answer space is tight.
• The tool does not generate prime-factorisation trees or Venn diagrams — it focuses on numeric answers only.
• Mixed mode cycles through the four question types in order, so a 16-question sheet will have exactly four of each type.