Free Grade 3 Working with Scale Factors Worksheets
Free Grade 3 worksheets for Working with Scale Factors: 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 scale factors
Identify working with scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with scale factors
Explain working with scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with scale factors
Calculate working with scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with scale factors
Compare working with scale factors 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 Scale Factors 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 18.[1]
- 3.List all the factors of 24.[1]
- 4.List all the factors of 36.[1]
- 5.Find the highest common factor (HCF) of 30 and 18.[2]
- 6.Find the highest common factor (HCF) of 56 and 32.[2]
- 7.Find the highest common factor (HCF) of 25 and 30.[2]
- 8.Find the highest common factor (HCF) of 42 and 49.[2]
- 9.Find the lowest common multiple (LCM) of 9 and 12.[3]
- 10.Find the lowest common multiple (LCM) of 4 and 8.[3]
- 11.Find the lowest common multiple (LCM) of 35 and 21.[3]
- 12.Find the lowest common multiple (LCM) of 24 and 30.[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, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
3. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
4. 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
5. 6
List factors of 30 and 18. The largest factor they share is 6.
6. 8
List factors of 56 and 32. The largest factor they share is 8.
7. 5
List factors of 25 and 30. The largest factor they share is 5.
8. 7
List factors of 42 and 49. The largest factor they share is 7.
9. 36
HCF(9, 12) = 3. LCM = 9 × 12 ÷ 3 = 36.
10. 8
HCF(4, 8) = 4. LCM = 4 × 8 ÷ 4 = 8.
11. 105
HCF(35, 21) = 7. LCM = 35 × 21 ÷ 7 = 105.
12. 120
HCF(24, 30) = 6. LCM = 24 × 30 ÷ 6 = 120.
Worked examples
List all the factors of 12.
- Find factor pairs that multiply to 12.
- 1 × 12
- 2 × 6
- 3 × 4
- Answer: 1, 2, 3, 4, 6, 12
Find the highest common factor (HCF) of 28 and 21.
- List factors of 28 and 21.
- The largest factor they share is 7.
- Answer: 7
Find the lowest common multiple (LCM) of 14 and 35.
- HCF(14, 35) = 7.
- LCM = 14 × 35 ÷ 7 = 70.
- Answer: 70
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.
Every free resource for Working with Scale Factors
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Frequently asked
- Is this Grade 3 Working with Scale Factors 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 Scale Factors, Inverse Proportion. 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 Working with Scale Factors?
- Move on to Scale Factors in Context, Direct Proportion, Inverse Proportion, Best Buy Problems, which build directly on this idea.
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