Free Grade 3 Introducing Factorising Word Problems Worksheets
Free Grade 3 worksheets for Introducing Factorising Word Problems: 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing factorising word problems
Explain introducing factorising word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising word problems
Calculate introducing factorising word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising word problems
Compare introducing factorising word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising word problems
Justify introducing factorising word problems 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 Word Problems 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 28.[1]
- 2.List all the factors of 36.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 20.[1]
- 5.Find the highest common factor (HCF) of 27 and 36.[2]
- 6.Find the highest common factor (HCF) of 14 and 14.[2]
- 7.Find the highest common factor (HCF) of 9 and 6.[2]
- 8.Find the highest common factor (HCF) of 24 and 16.[2]
- 9.Find the lowest common multiple (LCM) of 49 and 28.[3]
- 10.Find the lowest common multiple (LCM) of 28 and 35.[3]
- 11.Find the lowest common multiple (LCM) of 45 and 63.[3]
- 12.Find the lowest common multiple (LCM) of 24 and 36.[3]
Show answers and working
1. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
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, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
4. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
5. 9
List factors of 27 and 36. The largest factor they share is 9.
6. 14
List factors of 14 and 14. The largest factor they share is 14.
7. 3
List factors of 9 and 6. The largest factor they share is 3.
8. 8
List factors of 24 and 16. The largest factor they share is 8.
9. 196
HCF(49, 28) = 7. LCM = 49 × 28 ÷ 7 = 196.
10. 140
HCF(28, 35) = 7. LCM = 28 × 35 ÷ 7 = 140.
11. 315
HCF(45, 63) = 9. LCM = 45 × 63 ÷ 9 = 315.
12. 72
HCF(24, 36) = 12. LCM = 24 × 36 ÷ 12 = 72.
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 20 and 25.
- List factors of 20 and 25.
- The largest factor they share is 5.
- Answer: 5
Find the lowest common multiple (LCM) of 12 and 15.
- HCF(12, 15) = 3.
- LCM = 12 × 15 ÷ 3 = 60.
- Answer: 60
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
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Frequently asked
- Is this Grade 3 Introducing Factorising Word Problems 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 Techniques, 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 Word Problems?
- Move on to Introducing Factorising Common Errors, Working with Factorising, Factorising in Context, which build directly on this idea.
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