Free Grade 3 Working with HCF Lesson Plans
Free Grade 3 lesson plans 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
30 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 40.[1]
- 3.List all the factors of 30.[1]
- 4.List all the factors of 18.[1]
- 5.Find the highest common factor (HCF) of 14 and 14.[2]
- 6.Find the highest common factor (HCF) of 12 and 15.[2]
- 7.Find the highest common factor (HCF) of 12 and 18.[2]
- 8.Find the highest common factor (HCF) of 14 and 49.[2]
- 9.Find the highest common factor (HCF) of 10 and 10.[3]
- 10.Find the highest common factor (HCF) of 30 and 30.[3]
- 11.Find the lowest common multiple (LCM) of 16 and 12.[3]
- 12.Find the lowest common multiple (LCM) of 18 and 21.[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, 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, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
4. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
5. 14
List factors of 14 and 14. The largest factor they share is 14.
6. 3
List factors of 12 and 15. The largest factor they share is 3.
7. 6
List factors of 12 and 18. The largest factor they share is 6.
8. 7
List factors of 14 and 49. The largest factor they share is 7.
9. 10
List factors of 10 and 10. The largest factor they share is 10.
10. 30
List factors of 30 and 30. The largest factor they share is 30.
11. 48
HCF(16, 12) = 4. LCM = 16 × 12 ÷ 4 = 48.
12. 126
HCF(18, 21) = 3. LCM = 18 × 21 ÷ 3 = 126.
Worked examples
List all the factors of 24.
- Find factor pairs that multiply to 24.
- 1 × 24
- 2 × 12
- 3 × 8
- 4 × 6
- Answer: 1, 2, 3, 4, 6, 8, 12, 24
Find the highest common factor (HCF) of 25 and 30.
- List factors of 25 and 30.
- The largest factor they share is 5.
- Answer: 5
Find the lowest common multiple (LCM) of 10 and 14.
- HCF(10, 14) = 2.
- LCM = 10 × 14 ÷ 2 = 70.
- Answer: 70
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 HCF lesson plan really free?
- Yes. Every lesson plans 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 plan 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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