Free Grade 3 Introducing Factorising Common Errors Lessons
Free Grade 3 lessons for Introducing Factorising Common Errors: 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 introducing factorising common errors
Explain introducing factorising common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising common errors
Calculate introducing factorising common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising common errors
Compare introducing factorising common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising common errors
Justify introducing factorising common errors 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 Factorising Common Errors 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 12.[1]
- 2.List all the factors of 36.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 15 and 12.[2]
- 6.Find the highest common factor (HCF) of 35 and 30.[2]
- 7.Find the highest common factor (HCF) of 16 and 40.[2]
- 8.Find the highest common factor (HCF) of 48 and 16.[2]
- 9.Find the lowest common multiple (LCM) of 45 and 36.[3]
- 10.Find the lowest common multiple (LCM) of 25 and 10.[3]
- 11.Find the lowest common multiple (LCM) of 16 and 12.[3]
- 12.Find the lowest common multiple (LCM) of 12 and 28.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
2. 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
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 3
List factors of 15 and 12. The largest factor they share is 3.
6. 5
List factors of 35 and 30. The largest factor they share is 5.
7. 8
List factors of 16 and 40. The largest factor they share is 8.
8. 16
List factors of 48 and 16. The largest factor they share is 16.
9. 180
HCF(45, 36) = 9. LCM = 45 × 36 ÷ 9 = 180.
10. 50
HCF(25, 10) = 5. LCM = 25 × 10 ÷ 5 = 50.
11. 48
HCF(16, 12) = 4. LCM = 16 × 12 ÷ 4 = 48.
12. 84
HCF(12, 28) = 4. LCM = 12 × 28 ÷ 4 = 84.
Worked examples
List all the factors of 40.
- Find factor pairs that multiply to 40.
- 1 × 40
- 2 × 20
- 4 × 10
- 5 × 8
- Answer: 1, 2, 4, 5, 8, 10, 20, 40
Find the highest common factor (HCF) of 6 and 12.
- List factors of 6 and 12.
- The largest factor they share is 6.
- Answer: 6
Find the highest common factor (HCF) of 14 and 14.
- List factors of 14 and 14.
- The largest factor they share is 14.
- Answer: 14
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 Factorising Common Errors 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 Introducing Factorising Word Problems, Introducing Factorising Techniques, 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 Introducing Factorising Common Errors?
- Move on to Working with Factorising, Factorising in Context, which build directly on this idea.
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