Free Grade 3 Factorising Quizzes
Free Grade 3 quizzes for Factorising: 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain factorising
Explain factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factorising
Calculate factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factorising
Compare factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify factorising
Justify factorising 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 Factorising 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 18.[1]
- 3.List all the factors of 30.[1]
- 4.List all the factors of 36.[1]
- 5.Find the highest common factor (HCF) of 42 and 28.[2]
- 6.Find the highest common factor (HCF) of 40 and 56.[2]
- 7.Find the highest common factor (HCF) of 21 and 14.[2]
- 8.Find the highest common factor (HCF) of 21 and 18.[2]
- 9.Find the lowest common multiple (LCM) of 14 and 42.[3]
- 10.Find the lowest common multiple (LCM) of 14 and 6.[3]
- 11.Find the lowest common multiple (LCM) of 10 and 14.[3]
- 12.Find the lowest common multiple (LCM) of 28 and 49.[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, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
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, 4, 6, 9, 12, 18, 36
Find factor pairs that multiply to 36. 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6
5. 14
List factors of 42 and 28. The largest factor they share is 14.
6. 8
List factors of 40 and 56. The largest factor they share is 8.
7. 7
List factors of 21 and 14. The largest factor they share is 7.
8. 3
List factors of 21 and 18. The largest factor they share is 3.
9. 42
HCF(14, 42) = 14. LCM = 14 × 42 ÷ 14 = 42.
10. 42
HCF(14, 6) = 2. LCM = 14 × 6 ÷ 2 = 42.
11. 70
HCF(10, 14) = 2. LCM = 10 × 14 ÷ 2 = 70.
12. 196
HCF(28, 49) = 7. LCM = 28 × 49 ÷ 7 = 196.
Worked examples
List all the factors of 12.
- Find factor pairs that multiply to 12.
- 1 × 12
- 2 × 6
- 3 × 4
- Answer: 1, 2, 3, 4, 6, 12
Find the highest common factor (HCF) of 54 and 54.
- List factors of 54 and 54.
- The largest factor they share is 54.
- Answer: 54
Find the highest common factor (HCF) of 20 and 20.
- List factors of 20 and 20.
- The largest factor they share is 20.
- Answer: 20
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 Factorising
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Frequently asked
- Is this Grade 3 Factorising 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 Expanding Brackets, Substitution, Number Sense. 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 Factorising?
- Move on to Algebraic Fractions, Equations, Inequalities, Sequences, which build directly on this idea.
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