Free Grade 3 Factorising Lessons
Free Grade 3 lessons 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
Stretch
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 30.[1]
- 2.List all the factors of 18.[1]
- 3.List all the factors of 36.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 30 and 36.[2]
- 6.Find the highest common factor (HCF) of 14 and 10.[2]
- 7.Find the highest common factor (HCF) of 30 and 30.[2]
- 8.Find the highest common factor (HCF) of 28 and 20.[2]
- 9.Find the lowest common multiple (LCM) of 40 and 48.[3]
- 10.Find the highest common factor (HCF) of 42 and 42.[3]
- 11.Find the lowest common multiple (LCM) of 15 and 6.[3]
- 12.Find the lowest common multiple (LCM) of 6 and 4.[3]
Show answers and working
1. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
2. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
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, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
5. 6
List factors of 30 and 36. The largest factor they share is 6.
6. 2
List factors of 14 and 10. The largest factor they share is 2.
7. 30
List factors of 30 and 30. The largest factor they share is 30.
8. 4
List factors of 28 and 20. The largest factor they share is 4.
9. 240
HCF(40, 48) = 8. LCM = 40 × 48 ÷ 8 = 240.
10. 42
List factors of 42 and 42. The largest factor they share is 42.
11. 30
HCF(15, 6) = 3. LCM = 15 × 6 ÷ 3 = 30.
12. 12
HCF(6, 4) = 2. LCM = 6 × 4 ÷ 2 = 12.
Worked examples
List all the factors of 20.
- Find factor pairs that multiply to 20.
- 1 × 20
- 2 × 10
- 4 × 5
- Answer: 1, 2, 4, 5, 10, 20
Find the highest common factor (HCF) of 12 and 21.
- List factors of 12 and 21.
- The largest factor they share is 3.
- Answer: 3
Find the lowest common multiple (LCM) of 54 and 63.
- HCF(54, 63) = 9.
- LCM = 54 × 63 ÷ 9 = 378.
- Answer: 378
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 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 Expanding Brackets, Substitution, Number Sense. 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 Factorising?
- Move on to Algebraic Fractions, Equations, Inequalities, Sequences, which build directly on this idea.
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