Free Grade 3 HCF Lessons
Free Grade 3 lessons 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
15 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 40.[1]
- 2.List all the factors of 12.[1]
- 3.List all the factors of 36.[1]
- 4.List all the factors of 30.[1]
- 5.Find the highest common factor (HCF) of 63 and 27.[2]
- 6.Find the highest common factor (HCF) of 14 and 49.[2]
- 7.Find the highest common factor (HCF) of 27 and 27.[2]
- 8.Find the highest common factor (HCF) of 14 and 4.[2]
- 9.Find the lowest common multiple (LCM) of 14 and 35.[3]
- 10.Find the highest common factor (HCF) of 40 and 40.[3]
- 11.Find the lowest common multiple (LCM) of 9 and 21.[3]
- 12.Find the highest common factor (HCF) of 8 and 8.[3]
Show answers and working
1. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
2. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
3. 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
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. 9
List factors of 63 and 27. The largest factor they share is 9.
6. 7
List factors of 14 and 49. The largest factor they share is 7.
7. 27
List factors of 27 and 27. The largest factor they share is 27.
8. 2
List factors of 14 and 4. The largest factor they share is 2.
9. 70
HCF(14, 35) = 7. LCM = 14 × 35 ÷ 7 = 70.
10. 40
List factors of 40 and 40. The largest factor they share is 40.
11. 63
HCF(9, 21) = 3. LCM = 9 × 21 ÷ 3 = 63.
12. 8
List factors of 8 and 8. The largest factor they share is 8.
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 40 and 56.
- List factors of 40 and 56.
- The largest factor they share is 8.
- Answer: 8
Find the highest common factor (HCF) of 63 and 63.
- List factors of 63 and 63.
- The largest factor they share is 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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Learn — Meet the idea.
Practice — Build fluency.
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Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 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 Prime Factorisation, Prime Numbers, 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 HCF?
- Move on to LCM, Whole Numbers, Counting, Number Recognition, which build directly on this idea.
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