Free Grade 3 Working with HCF Lessons
Free Grade 3 lessons for Working with HCF: 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with hcf
Identify working with hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with hcf
Explain working with hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with hcf
Calculate working with hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with hcf
Compare working with hcf 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 HCF 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 20.[1]
- 2.List all the factors of 24.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 36.[1]
- 5.Find the highest common factor (HCF) of 54 and 36.[2]
- 6.Find the highest common factor (HCF) of 42 and 42.[2]
- 7.Find the highest common factor (HCF) of 25 and 30.[2]
- 8.Find the highest common factor (HCF) of 36 and 12.[2]
- 9.Find the lowest common multiple (LCM) of 56 and 24.[3]
- 10.Find the highest common factor (HCF) of 35 and 35.[3]
- 11.Find the lowest common multiple (LCM) of 24 and 16.[3]
- 12.Find the lowest common multiple (LCM) of 18 and 54.[3]
Show answers and working
1. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
2. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
3. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
4. 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
5. 18
List factors of 54 and 36. The largest factor they share is 18.
6. 42
List factors of 42 and 42. The largest factor they share is 42.
7. 5
List factors of 25 and 30. The largest factor they share is 5.
8. 12
List factors of 36 and 12. The largest factor they share is 12.
9. 168
HCF(56, 24) = 8. LCM = 56 × 24 ÷ 8 = 168.
10. 35
List factors of 35 and 35. The largest factor they share is 35.
11. 48
HCF(24, 16) = 8. LCM = 24 × 16 ÷ 8 = 48.
12. 54
HCF(18, 54) = 18. LCM = 18 × 54 ÷ 18 = 54.
Worked examples
List all the factors of 28.
- Find factor pairs that multiply to 28.
- 1 × 28
- 2 × 14
- 4 × 7
- Answer: 1, 2, 4, 7, 14, 28
Find the highest common factor (HCF) of 35 and 15.
- List factors of 35 and 15.
- The largest factor they share is 5.
- Answer: 5
Find the lowest common multiple (LCM) of 6 and 9.
- HCF(6, 9) = 3.
- LCM = 6 × 9 ÷ 3 = 18.
- Answer: 18
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 Working with HCF
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Frequently asked
- Is this Grade 3 Working with HCF 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 HCF, Prime Factorisation. 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 HCF?
- Move on to HCF in Context, Factors, Multiples, Prime Numbers, which build directly on this idea.
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