Free Grade 3 Prime Factorisation in Context Worksheets
Free Grade 3 worksheets for Prime Factorisation in Context: 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
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain prime factorisation in context
Explain prime factorisation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate prime factorisation in context
Calculate prime factorisation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare prime factorisation in context
Compare prime factorisation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify prime factorisation in context
Justify prime factorisation in context 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 in Context 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 18.[1]
- 2.List all the factors of 30.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 40 and 32.[2]
- 6.Find the highest common factor (HCF) of 45 and 63.[2]
- 7.Find the highest common factor (HCF) of 42 and 21.[2]
- 8.Find the highest common factor (HCF) of 54 and 27.[2]
- 9.Find the lowest common multiple (LCM) of 21 and 42.[3]
- 10.Find the lowest common multiple (LCM) of 20 and 35.[3]
- 11.Find the lowest common multiple (LCM) of 10 and 15.[3]
- 12.Find the highest common factor (HCF) of 6 and 6.[3]
Show answers and working
1. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
2. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 8
List factors of 40 and 32. The largest factor they share is 8.
6. 9
List factors of 45 and 63. The largest factor they share is 9.
7. 21
List factors of 42 and 21. The largest factor they share is 21.
8. 27
List factors of 54 and 27. The largest factor they share is 27.
9. 42
HCF(21, 42) = 21. LCM = 21 × 42 ÷ 21 = 42.
10. 140
HCF(20, 35) = 5. LCM = 20 × 35 ÷ 5 = 140.
11. 30
HCF(10, 15) = 5. LCM = 10 × 15 ÷ 5 = 30.
12. 6
List factors of 6 and 6. The largest factor they share is 6.
Worked examples
List all the factors of 40.
- Find factor pairs that multiply to 40.
- 1 × 40
- 2 × 20
- 4 × 10
- 5 × 8
- Answer: 1, 2, 4, 5, 8, 10, 20, 40
Find the highest common factor (HCF) of 18 and 30.
- List factors of 18 and 30.
- The largest factor they share is 6.
- Answer: 6
Find the lowest common multiple (LCM) of 15 and 6.
- HCF(15, 6) = 3.
- LCM = 15 × 6 ÷ 3 = 30.
- Answer: 30
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.
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Frequently asked
- Is this Grade 3 Prime Factorisation in Context 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 Working with Prime Factorisation, Introducing Prime Factorisation, Prime Numbers. 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 in Context?
- Move on to Factors, Multiples, Prime Numbers, HCF, which build directly on this idea.
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