Free Grade 3 Scalar Multiples Worksheets
Free Grade 3 worksheets for 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain scalar multiples
Explain scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate scalar multiples
Calculate scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare scalar multiples
Compare scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify scalar multiples
Justify 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 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 20.[1]
- 2.List all the factors of 12.[1]
- 3.List all the factors of 36.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 63 and 36.[2]
- 6.Find the highest common factor (HCF) of 42 and 35.[2]
- 7.Find the highest common factor (HCF) of 28 and 16.[2]
- 8.Find the highest common factor (HCF) of 28 and 35.[2]
- 9.Find the lowest common multiple (LCM) of 36 and 42.[3]
- 10.Find the lowest common multiple (LCM) of 18 and 54.[3]
- 11.Find the highest common factor (HCF) of 14 and 14.[3]
- 12.Find the highest common factor (HCF) of 20 and 20.[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, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
3. 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
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 9
List factors of 63 and 36. The largest factor they share is 9.
6. 7
List factors of 42 and 35. The largest factor they share is 7.
7. 4
List factors of 28 and 16. The largest factor they share is 4.
8. 7
List factors of 28 and 35. The largest factor they share is 7.
9. 252
HCF(36, 42) = 6. LCM = 36 × 42 ÷ 6 = 252.
10. 54
HCF(18, 54) = 18. LCM = 18 × 54 ÷ 18 = 54.
11. 14
List factors of 14 and 14. The largest factor they share is 14.
12. 20
List factors of 20 and 20. The largest factor they share is 20.
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 42 and 42.
- List factors of 42 and 42.
- The largest factor they share is 42.
- Answer: 42
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.
Every free resource for Scalar Multiples
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Frequently asked
- Is this Grade 3 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 Adding Vectors, Vector Notation, Calculus. 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 Scalar Multiples?
- Move on to Magnitude of a Vector, Vector Geometry, which build directly on this idea.
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