Free Grade 3 HCF in Context Quizzes
Free Grade 3 quizzes for HCF in Context: 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.
- UnderstandExplain hcf in context
Explain hcf in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate hcf in context
Calculate hcf in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare hcf in context
Compare hcf in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify hcf in context
Justify hcf in context 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 in Context 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 12.[1]
- 3.List all the factors of 36.[1]
- 4.List all the factors of 20.[1]
- 5.Find the highest common factor (HCF) of 25 and 20.[2]
- 6.Find the highest common factor (HCF) of 54 and 18.[2]
- 7.Find the highest common factor (HCF) of 20 and 8.[2]
- 8.Find the highest common factor (HCF) of 8 and 6.[2]
- 9.Find the lowest common multiple (LCM) of 10 and 4.[3]
- 10.Find the lowest common multiple (LCM) of 40 and 24.[3]
- 11.Find the lowest common multiple (LCM) of 27 and 18.[3]
- 12.Find the lowest common multiple (LCM) of 54 and 45.[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, 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, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
5. 5
List factors of 25 and 20. The largest factor they share is 5.
6. 18
List factors of 54 and 18. The largest factor they share is 18.
7. 4
List factors of 20 and 8. The largest factor they share is 4.
8. 2
List factors of 8 and 6. The largest factor they share is 2.
9. 20
HCF(10, 4) = 2. LCM = 10 × 4 ÷ 2 = 20.
10. 120
HCF(40, 24) = 8. LCM = 40 × 24 ÷ 8 = 120.
11. 54
HCF(27, 18) = 9. LCM = 27 × 18 ÷ 9 = 54.
12. 270
HCF(54, 45) = 9. LCM = 54 × 45 ÷ 9 = 270.
Worked examples
List all the factors of 40.
- Find factor pairs that multiply to 40.
- 1 × 40
- 2 × 20
- 4 × 10
- 5 × 8
- Answer: 1, 2, 4, 5, 8, 10, 20, 40
Find the highest common factor (HCF) of 20 and 30.
- List factors of 20 and 30.
- The largest factor they share is 10.
- Answer: 10
Find the lowest common multiple (LCM) of 35 and 42.
- HCF(35, 42) = 7.
- LCM = 35 × 42 ÷ 7 = 210.
- Answer: 210
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 in Context
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Frequently asked
- Is this Grade 3 HCF in Context quiz really free?
- Yes. Every quizzes 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 Working with HCF, Introducing HCF, Prime Factorisation. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 in Context?
- Move on to Factors, Multiples, Prime Numbers, Prime Factorisation, which build directly on this idea.
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