Free Grade 3 Working with Factorising Lesson Plans
Free Grade 3 lesson plans for Working with 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
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with factorising
Identify working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with factorising
Explain working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with factorising
Calculate working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with factorising
Compare working with 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 Working with 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 24.[1]
- 2.List all the factors of 18.[1]
- 3.List all the factors of 28.[1]
- 4.List all the factors of 40.[1]
- 5.Find the highest common factor (HCF) of 54 and 45.[2]
- 6.Find the highest common factor (HCF) of 24 and 30.[2]
- 7.Find the highest common factor (HCF) of 9 and 21.[2]
- 8.Find the highest common factor (HCF) of 28 and 12.[2]
- 9.Find the lowest common multiple (LCM) of 20 and 15.[3]
- 10.Find the lowest common multiple (LCM) of 28 and 14.[3]
- 11.Find the lowest common multiple (LCM) of 56 and 40.[3]
- 12.Find the highest common factor (HCF) of 30 and 30.[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, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
4. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
5. 9
List factors of 54 and 45. The largest factor they share is 9.
6. 6
List factors of 24 and 30. The largest factor they share is 6.
7. 3
List factors of 9 and 21. The largest factor they share is 3.
8. 4
List factors of 28 and 12. The largest factor they share is 4.
9. 60
HCF(20, 15) = 5. LCM = 20 × 15 ÷ 5 = 60.
10. 28
HCF(28, 14) = 14. LCM = 28 × 14 ÷ 14 = 28.
11. 280
HCF(56, 40) = 8. LCM = 56 × 40 ÷ 8 = 280.
12. 30
List factors of 30 and 30. The largest factor they share is 30.
Worked examples
List all the factors of 30.
- Find factor pairs that multiply to 30.
- 1 × 30
- 2 × 15
- 3 × 10
- 5 × 6
- Answer: 1, 2, 3, 5, 6, 10, 15, 30
Find the highest common factor (HCF) of 40 and 56.
- List factors of 40 and 56.
- The largest factor they share is 8.
- Answer: 8
Find the lowest common multiple (LCM) of 40 and 32.
- HCF(40, 32) = 8.
- LCM = 40 × 32 ÷ 8 = 160.
- Answer: 160
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 Working with Factorising lesson plan really free?
- Yes. Every lesson plans 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 Introducing Factorising, Expanding Brackets. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Working with Factorising?
- Move on to Factorising in Context, Using Letters for Numbers, Collecting Like Terms, Substitution, which build directly on this idea.
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