Free Grade 3 Introducing Scalar Multiples Essentials Worksheets
Free Grade 3 worksheets for Introducing Scalar Multiples Essentials: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing scalar multiples essentials
Explain introducing scalar multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing scalar multiples essentials
Calculate introducing scalar multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing scalar multiples essentials
Compare introducing scalar multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing scalar multiples essentials
Justify introducing scalar multiples essentials 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 Scalar Multiples Essentials 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 12.[1]
- 2.List all the factors of 40.[1]
- 3.List all the factors of 36.[1]
- 4.List all the factors of 20.[1]
- 5.Find the highest common factor (HCF) of 20 and 30.[2]
- 6.Find the highest common factor (HCF) of 10 and 8.[2]
- 7.Find the highest common factor (HCF) of 36 and 36.[2]
- 8.Find the highest common factor (HCF) of 12 and 6.[2]
- 9.Find the lowest common multiple (LCM) of 14 and 42.[3]
- 10.Find the lowest common multiple (LCM) of 36 and 27.[3]
- 11.Find the lowest common multiple (LCM) of 20 and 25.[3]
- 12.Find the lowest common multiple (LCM) of 12 and 42.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
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, 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, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
5. 10
List factors of 20 and 30. The largest factor they share is 10.
6. 2
List factors of 10 and 8. The largest factor they share is 2.
7. 36
List factors of 36 and 36. The largest factor they share is 36.
8. 6
List factors of 12 and 6. The largest factor they share is 6.
9. 42
HCF(14, 42) = 14. LCM = 14 × 42 ÷ 14 = 42.
10. 108
HCF(36, 27) = 9. LCM = 36 × 27 ÷ 9 = 108.
11. 100
HCF(20, 25) = 5. LCM = 20 × 25 ÷ 5 = 100.
12. 84
HCF(12, 42) = 6. LCM = 12 × 42 ÷ 6 = 84.
Worked examples
List all the factors of 30.
- Find factor pairs that multiply to 30.
- 1 × 30
- 2 × 15
- 3 × 10
- 5 × 6
- Answer: 1, 2, 3, 5, 6, 10, 15, 30
Find the highest common factor (HCF) of 49 and 28.
- List factors of 49 and 28.
- The largest factor they share is 7.
- Answer: 7
Find the lowest common multiple (LCM) of 24 and 32.
- HCF(24, 32) = 8.
- LCM = 24 × 32 ÷ 8 = 96.
- Answer: 96
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 Scalar Multiples Essentials 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. 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 Scalar Multiples Essentials?
- Move on to Introducing Scalar Multiples Techniques, Introducing Scalar Multiples Word Problems, Introducing Scalar Multiples Common Errors, Working with Scalar Multiples, which build directly on this idea.
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