Free Grade 3 Prime Factorisation Lessons
Free Grade 3 lessons 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
25 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 28.[1]
- 2.List all the factors of 30.[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 20 and 16.[2]
- 6.Find the highest common factor (HCF) of 45 and 45.[2]
- 7.Find the highest common factor (HCF) of 18 and 45.[2]
- 8.Find the highest common factor (HCF) of 24 and 36.[2]
- 9.Find the lowest common multiple (LCM) of 18 and 36.[3]
- 10.Find the lowest common multiple (LCM) of 56 and 24.[3]
- 11.Find the lowest common multiple (LCM) of 21 and 15.[3]
- 12.Find the lowest common multiple (LCM) of 12 and 18.[3]
Show answers and working
1. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
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, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
5. 4
List factors of 20 and 16. The largest factor they share is 4.
6. 45
List factors of 45 and 45. The largest factor they share is 45.
7. 9
List factors of 18 and 45. The largest factor they share is 9.
8. 12
List factors of 24 and 36. The largest factor they share is 12.
9. 36
HCF(18, 36) = 18. LCM = 18 × 36 ÷ 18 = 36.
10. 168
HCF(56, 24) = 8. LCM = 56 × 24 ÷ 8 = 168.
11. 105
HCF(21, 15) = 3. LCM = 21 × 15 ÷ 3 = 105.
12. 36
HCF(12, 18) = 6. LCM = 12 × 18 ÷ 6 = 36.
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 27.
- List factors of 18 and 27.
- The largest factor they share is 9.
- Answer: 9
Find the lowest common multiple (LCM) of 42 and 21.
- HCF(42, 21) = 21.
- LCM = 42 × 21 ÷ 21 = 42.
- Answer: 42
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 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 Prime Numbers, Multiples, Proportion. 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?
- Move on to HCF, LCM, Whole Numbers, Counting, which build directly on this idea.
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