Free Grade 3 Prime Factorisation Worksheets
Free Grade 3 worksheets for Prime Factorisation: 12 real questions with a full answer key and worked solutions. Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
Free
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify prime factorisation
Identify prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain prime factorisation
Explain prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate prime factorisation
Calculate prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare prime factorisation
Compare prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Prime Factorisation works
Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.List all the factors of 24.[1]
- 2.List all the factors of 18.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 12.[1]
- 5.Find the highest common factor (HCF) of 24 and 42.[2]
- 6.Find the highest common factor (HCF) of 12 and 24.[2]
- 7.Find the highest common factor (HCF) of 48 and 16.[2]
- 8.Find the highest common factor (HCF) of 18 and 18.[2]
- 9.Find the lowest common multiple (LCM) of 20 and 30.[3]
- 10.Find the highest common factor (HCF) of 32 and 32.[3]
- 11.Find the lowest common multiple (LCM) of 40 and 16.[3]
- 12.Find the highest common factor (HCF) of 27 and 27.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
2. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
5. 6
List factors of 24 and 42. The largest factor they share is 6.
6. 12
List factors of 12 and 24. The largest factor they share is 12.
7. 16
List factors of 48 and 16. The largest factor they share is 16.
8. 18
List factors of 18 and 18. The largest factor they share is 18.
9. 60
HCF(20, 30) = 10. LCM = 20 × 30 ÷ 10 = 60.
10. 32
List factors of 32 and 32. The largest factor they share is 32.
11. 80
HCF(40, 16) = 8. LCM = 40 × 16 ÷ 8 = 80.
12. 27
List factors of 27 and 27. The largest factor they share is 27.
Worked examples
List all the factors of 30.
- Find factor pairs that multiply to 30.
- 1 × 30
- 2 × 15
- 3 × 10
- 5 × 6
- Answer: 1, 2, 3, 5, 6, 10, 15, 30
Find the highest common factor (HCF) of 6 and 8.
- List factors of 6 and 8.
- The largest factor they share is 2.
- Answer: 2
Find the lowest common multiple (LCM) of 18 and 63.
- HCF(18, 63) = 9.
- LCM = 18 × 63 ÷ 9 = 126.
- Answer: 126
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up factors and multiples.
Correction: Factors are Few (they fit inside), multiples are Many (they go on forever).
Misses factor pairs.
Correction: Work through 1, 2, 3… in order until the pairs meet.
Teacher tips
- · Use factor rainbows to show pairs.
Parent tips
- · Ask how many ways 24 sweets can be put into equal bags.
Real-life applications
- · Arranging chairs in equal rows, syncing bus timetables (LCM).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Prime Factorisation
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Frequently asked
- Is this Grade 3 Prime Factorisation worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Prime Numbers, Multiples, Proportion. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Prime Factorisation?
- Move on to HCF, LCM, Whole Numbers, Counting, which build directly on this idea.
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