Free Grade 3 HCF Lesson Plans
Free Grade 3 lesson plans for 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain hcf
Explain hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate hcf
Calculate hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare hcf
Compare hcf accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify hcf
Justify 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 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 28.[1]
- 2.List all the factors of 24.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 20.[1]
- 5.Find the highest common factor (HCF) of 42 and 42.[2]
- 6.Find the highest common factor (HCF) of 12 and 12.[2]
- 7.Find the highest common factor (HCF) of 27 and 63.[2]
- 8.Find the highest common factor (HCF) of 25 and 20.[2]
- 9.Find the lowest common multiple (LCM) of 16 and 24.[3]
- 10.Find the lowest common multiple (LCM) of 14 and 4.[3]
- 11.Find the lowest common multiple (LCM) of 6 and 12.[3]
- 12.Find the lowest common multiple (LCM) of 28 and 42.[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, 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, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
5. 42
List factors of 42 and 42. The largest factor they share is 42.
6. 12
List factors of 12 and 12. The largest factor they share is 12.
7. 9
List factors of 27 and 63. The largest factor they share is 9.
8. 5
List factors of 25 and 20. The largest factor they share is 5.
9. 48
HCF(16, 24) = 8. LCM = 16 × 24 ÷ 8 = 48.
10. 28
HCF(14, 4) = 2. LCM = 14 × 4 ÷ 2 = 28.
11. 12
HCF(6, 12) = 6. LCM = 6 × 12 ÷ 6 = 12.
12. 84
HCF(28, 42) = 14. LCM = 28 × 42 ÷ 14 = 84.
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 40 and 32.
- List factors of 40 and 32.
- The largest factor they share is 8.
- Answer: 8
Find the lowest common multiple (LCM) of 9 and 21.
- HCF(9, 21) = 3.
- LCM = 9 × 21 ÷ 3 = 63.
- Answer: 63
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 HCF
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Frequently asked
- Is this Grade 3 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 Prime Factorisation, Prime Numbers, Proportion. 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 HCF?
- Move on to LCM, Whole Numbers, Counting, Number Recognition, which build directly on this idea.
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