Free Grade 3 Working with Prime Factorisation Lessons
Free Grade 3 lessons for Working with 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with prime factorisation
Identify working with prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with prime factorisation
Explain working with prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with prime factorisation
Calculate working with prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with prime factorisation
Compare working with 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 Working with 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 36.[1]
- 2.List all the factors of 40.[1]
- 3.List all the factors of 28.[1]
- 4.List all the factors of 30.[1]
- 5.Find the highest common factor (HCF) of 20 and 28.[2]
- 6.Find the highest common factor (HCF) of 4 and 14.[2]
- 7.Find the highest common factor (HCF) of 18 and 12.[2]
- 8.Find the highest common factor (HCF) of 42 and 21.[2]
- 9.Find the lowest common multiple (LCM) of 49 and 35.[3]
- 10.Find the lowest common multiple (LCM) of 20 and 35.[3]
- 11.Find the lowest common multiple (LCM) of 20 and 15.[3]
- 12.Find the lowest common multiple (LCM) of 8 and 6.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 9, 12, 18, 36
Find factor pairs that multiply to 36. 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6
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, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
4. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
5. 4
List factors of 20 and 28. The largest factor they share is 4.
6. 2
List factors of 4 and 14. The largest factor they share is 2.
7. 6
List factors of 18 and 12. The largest factor they share is 6.
8. 21
List factors of 42 and 21. The largest factor they share is 21.
9. 245
HCF(49, 35) = 7. LCM = 49 × 35 ÷ 7 = 245.
10. 140
HCF(20, 35) = 5. LCM = 20 × 35 ÷ 5 = 140.
11. 60
HCF(20, 15) = 5. LCM = 20 × 15 ÷ 5 = 60.
12. 24
HCF(8, 6) = 2. LCM = 8 × 6 ÷ 2 = 24.
Worked examples
List all the factors of 18.
- Find factor pairs that multiply to 18.
- 1 × 18
- 2 × 9
- 3 × 6
- Answer: 1, 2, 3, 6, 9, 18
Find the highest common factor (HCF) of 6 and 14.
- List factors of 6 and 14.
- The largest factor they share is 2.
- Answer: 2
Find the lowest common multiple (LCM) of 28 and 14.
- HCF(28, 14) = 14.
- LCM = 28 × 14 ÷ 14 = 28.
- Answer: 28
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 Working with 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 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 Working with Prime Factorisation?
- Move on to Prime Factorisation in Context, Factors, Multiples, Prime Numbers, which build directly on this idea.
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