Free Grade 3 Introducing Factorising Techniques Worksheets
Free Grade 3 worksheets for Introducing Factorising Techniques: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing factorising techniques
Explain introducing factorising techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising techniques
Calculate introducing factorising techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising techniques
Compare introducing factorising techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising techniques
Justify introducing factorising techniques 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 Techniques 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 20.[1]
- 2.List all the factors of 24.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 20 and 20.[2]
- 6.Find the highest common factor (HCF) of 20 and 25.[2]
- 7.Find the highest common factor (HCF) of 36 and 36.[2]
- 8.Find the highest common factor (HCF) of 20 and 35.[2]
- 9.Find the lowest common multiple (LCM) of 15 and 35.[3]
- 10.Find the lowest common multiple (LCM) of 18 and 63.[3]
- 11.Find the lowest common multiple (LCM) of 6 and 15.[3]
- 12.Find the lowest common multiple (LCM) of 8 and 12.[3]
Show answers and working
1. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
2. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
3. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 20
List factors of 20 and 20. The largest factor they share is 20.
6. 5
List factors of 20 and 25. The largest factor they share is 5.
7. 36
List factors of 36 and 36. The largest factor they share is 36.
8. 5
List factors of 20 and 35. The largest factor they share is 5.
9. 105
HCF(15, 35) = 5. LCM = 15 × 35 ÷ 5 = 105.
10. 126
HCF(18, 63) = 9. LCM = 18 × 63 ÷ 9 = 126.
11. 30
HCF(6, 15) = 3. LCM = 6 × 15 ÷ 3 = 30.
12. 24
HCF(8, 12) = 4. LCM = 8 × 12 ÷ 4 = 24.
Worked examples
List all the factors of 18.
- Find factor pairs that multiply to 18.
- 1 × 18
- 2 × 9
- 3 × 6
- Answer: 1, 2, 3, 6, 9, 18
Find the highest common factor (HCF) of 21 and 18.
- List factors of 21 and 18.
- The largest factor they share is 3.
- Answer: 3
Find the lowest common multiple (LCM) of 10 and 15.
- HCF(10, 15) = 5.
- LCM = 10 × 15 ÷ 5 = 30.
- Answer: 30
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 Techniques worksheet really free?
- Yes. Every worksheets 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 Essentials, Expanding Brackets. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Techniques?
- Move on to Introducing Factorising Word Problems, Introducing Factorising Common Errors, Working with Factorising, Factorising in Context, which build directly on this idea.
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