Free Grade 3 Factorising in Context Lessons
Free Grade 3 lessons for Factorising 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain factorising in context
Explain factorising in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factorising in context
Calculate factorising in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factorising in context
Compare factorising in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify factorising in context
Justify factorising 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 Factorising 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 24.[1]
- 2.List all the factors of 18.[1]
- 3.List all the factors of 40.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 20 and 10.[2]
- 6.Find the highest common factor (HCF) of 21 and 35.[2]
- 7.Find the highest common factor (HCF) of 6 and 12.[2]
- 8.Find the highest common factor (HCF) of 24 and 42.[2]
- 9.Find the lowest common multiple (LCM) of 4 and 6.[3]
- 10.Find the lowest common multiple (LCM) of 40 and 32.[3]
- 11.Find the lowest common multiple (LCM) of 36 and 42.[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, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
3. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 10
List factors of 20 and 10. The largest factor they share is 10.
6. 7
List factors of 21 and 35. The largest factor they share is 7.
7. 6
List factors of 6 and 12. The largest factor they share is 6.
8. 6
List factors of 24 and 42. The largest factor they share is 6.
9. 12
HCF(4, 6) = 2. LCM = 4 × 6 ÷ 2 = 12.
10. 160
HCF(40, 32) = 8. LCM = 40 × 32 ÷ 8 = 160.
11. 252
HCF(36, 42) = 6. LCM = 36 × 42 ÷ 6 = 252.
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 35 and 30.
- List factors of 35 and 30.
- The largest factor they share is 5.
- Answer: 5
Find the lowest common multiple (LCM) of 27 and 18.
- HCF(27, 18) = 9.
- LCM = 27 × 18 ÷ 9 = 54.
- Answer: 54
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 Factorising in Context 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 Working with Factorising, Introducing Factorising, Expanding Brackets. 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 in Context?
- Move on to Using Letters for Numbers, Collecting Like Terms, Substitution, Expanding Brackets, which build directly on this idea.
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