Free Grade 3 Working with Scalar Multiples Worksheets
Free Grade 3 worksheets for Working with Scalar Multiples: 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 working with scalar multiples
Explain working with scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with scalar multiples
Calculate working with scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with scalar multiples
Compare working with scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with scalar multiples
Justify working with scalar multiples 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 Scalar Multiples 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 30.[1]
- 2.List all the factors of 40.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 24 and 40.[2]
- 6.Find the highest common factor (HCF) of 30 and 35.[2]
- 7.Find the highest common factor (HCF) of 28 and 12.[2]
- 8.Find the highest common factor (HCF) of 42 and 49.[2]
- 9.Find the lowest common multiple (LCM) of 28 and 35.[3]
- 10.Find the lowest common multiple (LCM) of 24 and 56.[3]
- 11.Find the lowest common multiple (LCM) of 10 and 20.[3]
- 12.Find the lowest common multiple (LCM) of 24 and 42.[3]
Show answers and working
1. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
2. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
5. 8
List factors of 24 and 40. The largest factor they share is 8.
6. 5
List factors of 30 and 35. The largest factor they share is 5.
7. 4
List factors of 28 and 12. The largest factor they share is 4.
8. 7
List factors of 42 and 49. The largest factor they share is 7.
9. 140
HCF(28, 35) = 7. LCM = 28 × 35 ÷ 7 = 140.
10. 168
HCF(24, 56) = 8. LCM = 24 × 56 ÷ 8 = 168.
11. 20
HCF(10, 20) = 10. LCM = 10 × 20 ÷ 10 = 20.
12. 168
HCF(24, 42) = 6. LCM = 24 × 42 ÷ 6 = 168.
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 30 and 12.
- List factors of 30 and 12.
- The largest factor they share is 6.
- Answer: 6
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 Working with Scalar Multiples 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 Scalar Multiples, Adding Vectors. 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 Scalar Multiples?
- Move on to Scalar Multiples in Context, Vector Notation, Adding Vectors, Magnitude of a Vector, which build directly on this idea.
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