Free Grade 3 Introducing Factorising Essentials Lessons
Free Grade 3 lessons for Introducing Factorising Essentials: 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing factorising essentials
Explain introducing factorising essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising essentials
Calculate introducing factorising essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising essentials
Compare introducing factorising essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising essentials
Justify introducing factorising essentials 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 Essentials 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 20.[1]
- 4.List all the factors of 40.[1]
- 5.Find the highest common factor (HCF) of 20 and 28.[2]
- 6.Find the highest common factor (HCF) of 8 and 4.[2]
- 7.Find the highest common factor (HCF) of 15 and 15.[2]
- 8.Find the highest common factor (HCF) of 10 and 14.[2]
- 9.Find the lowest common multiple (LCM) of 16 and 24.[3]
- 10.Find the lowest common multiple (LCM) of 49 and 14.[3]
- 11.Find the highest common factor (HCF) of 9 and 9.[3]
- 12.Find the lowest common multiple (LCM) of 18 and 9.[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, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
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. 4
List factors of 20 and 28. The largest factor they share is 4.
6. 4
List factors of 8 and 4. The largest factor they share is 4.
7. 15
List factors of 15 and 15. The largest factor they share is 15.
8. 2
List factors of 10 and 14. The largest factor they share is 2.
9. 48
HCF(16, 24) = 8. LCM = 16 × 24 ÷ 8 = 48.
10. 98
HCF(49, 14) = 7. LCM = 49 × 14 ÷ 7 = 98.
11. 9
List factors of 9 and 9. The largest factor they share is 9.
12. 18
HCF(18, 9) = 9. LCM = 18 × 9 ÷ 9 = 18.
Worked examples
List all the factors of 28.
- Find factor pairs that multiply to 28.
- 1 × 28
- 2 × 14
- 4 × 7
- Answer: 1, 2, 4, 7, 14, 28
Find the highest common factor (HCF) of 20 and 16.
- List factors of 20 and 16.
- The largest factor they share is 4.
- Answer: 4
Find the highest common factor (HCF) of 12 and 12.
- List factors of 12 and 12.
- The largest factor they share is 12.
- Answer: 12
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 Essentials 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. 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 Essentials?
- Move on to Introducing Factorising Techniques, Introducing Factorising Word Problems, Introducing Factorising Common Errors, Working with Factorising, which build directly on this idea.
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