Free Grade 3 Prime Factorisation in Context Lessons
Free Grade 3 lessons 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
30 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 12.[1]
- 2.List all the factors of 40.[1]
- 3.List all the factors of 18.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 35 and 10.[2]
- 6.Find the highest common factor (HCF) of 15 and 30.[2]
- 7.Find the highest common factor (HCF) of 36 and 36.[2]
- 8.Find the highest common factor (HCF) of 20 and 12.[2]
- 9.Find the lowest common multiple (LCM) of 42 and 21.[3]
- 10.Find the lowest common multiple (LCM) of 6 and 12.[3]
- 11.Find the lowest common multiple (LCM) of 36 and 45.[3]
- 12.Find the lowest common multiple (LCM) of 56 and 32.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
2. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
3. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
4. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
5. 5
List factors of 35 and 10. The largest factor they share is 5.
6. 15
List factors of 15 and 30. The largest factor they share is 15.
7. 36
List factors of 36 and 36. The largest factor they share is 36.
8. 4
List factors of 20 and 12. The largest factor they share is 4.
9. 42
HCF(42, 21) = 21. LCM = 42 × 21 ÷ 21 = 42.
10. 12
HCF(6, 12) = 6. LCM = 6 × 12 ÷ 6 = 12.
11. 180
HCF(36, 45) = 9. LCM = 36 × 45 ÷ 9 = 180.
12. 224
HCF(56, 32) = 8. LCM = 56 × 32 ÷ 8 = 224.
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 21 and 6.
- List factors of 21 and 6.
- The largest factor they share is 3.
- Answer: 3
Find the highest common factor (HCF) of 14 and 14.
- List factors of 14 and 14.
- The largest factor they share is 14.
- Answer: 14
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 lesson really free?
- Yes. Every lessons 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 lesson 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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