Free Grade 3 Introducing Prime Factorisation Quizzes
Free Grade 3 quizzes for Introducing Prime Factorisation: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing prime factorisation
Identify introducing prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing prime factorisation
Explain introducing prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing prime factorisation
Calculate introducing prime factorisation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing prime factorisation
Compare introducing prime factorisation 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 Introducing Prime Factorisation 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 24.[1]
- 2.List all the factors of 28.[1]
- 3.List all the factors of 18.[1]
- 4.List all the factors of 12.[1]
- 5.Find the highest common factor (HCF) of 36 and 42.[2]
- 6.Find the highest common factor (HCF) of 8 and 6.[2]
- 7.Find the highest common factor (HCF) of 12 and 24.[2]
- 8.Find the highest common factor (HCF) of 28 and 12.[2]
- 9.Find the lowest common multiple (LCM) of 20 and 30.[3]
- 10.Find the lowest common multiple (LCM) of 16 and 24.[3]
- 11.Find the lowest common multiple (LCM) of 12 and 6.[3]
- 12.Find the lowest common multiple (LCM) of 6 and 4.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
2. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
3. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
4. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
5. 6
List factors of 36 and 42. The largest factor they share is 6.
6. 2
List factors of 8 and 6. The largest factor they share is 2.
7. 12
List factors of 12 and 24. The largest factor they share is 12.
8. 4
List factors of 28 and 12. The largest factor they share is 4.
9. 60
HCF(20, 30) = 10. LCM = 20 × 30 ÷ 10 = 60.
10. 48
HCF(16, 24) = 8. LCM = 16 × 24 ÷ 8 = 48.
11. 12
HCF(12, 6) = 6. LCM = 12 × 6 ÷ 6 = 12.
12. 12
HCF(6, 4) = 2. LCM = 6 × 4 ÷ 2 = 12.
Worked examples
List all the factors of 36.
- Find factor pairs that multiply to 36.
- 1 × 36
- 2 × 18
- 3 × 12
- 4 × 9
- 6 × 6
- Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Find the highest common factor (HCF) of 10 and 8.
- List factors of 10 and 8.
- The largest factor they share is 2.
- Answer: 2
Find the highest common factor (HCF) of 36 and 36.
- List factors of 36 and 36.
- The largest factor they share is 36.
- Answer: 36
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 Introducing Prime Factorisation 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 Prime Numbers. 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 Introducing Prime Factorisation?
- Move on to Working with Prime Factorisation, Prime Factorisation in Context, Factors, Multiples, which build directly on this idea.
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