Free Grade 3 Introducing Scalar Multiples Quizzes
Free Grade 3 quizzes for Introducing 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
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing scalar multiples
Explain introducing scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing scalar multiples
Calculate introducing scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing scalar multiples
Compare introducing scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing scalar multiples
Justify introducing 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 Introducing 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 24.[1]
- 2.List all the factors of 12.[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 54 and 36.[2]
- 6.Find the highest common factor (HCF) of 21 and 35.[2]
- 7.Find the highest common factor (HCF) of 15 and 30.[2]
- 8.Find the highest common factor (HCF) of 20 and 20.[2]
- 9.Find the highest common factor (HCF) of 36 and 36.[3]
- 10.Find the lowest common multiple (LCM) of 10 and 6.[3]
- 11.Find the lowest common multiple (LCM) of 12 and 24.[3]
- 12.Find the lowest common multiple (LCM) of 49 and 21.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
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, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
5. 18
List factors of 54 and 36. The largest factor they share is 18.
6. 7
List factors of 21 and 35. The largest factor they share is 7.
7. 15
List factors of 15 and 30. The largest factor they share is 15.
8. 20
List factors of 20 and 20. The largest factor they share is 20.
9. 36
List factors of 36 and 36. The largest factor they share is 36.
10. 30
HCF(10, 6) = 2. LCM = 10 × 6 ÷ 2 = 30.
11. 24
HCF(12, 24) = 12. LCM = 12 × 24 ÷ 12 = 24.
12. 147
HCF(49, 21) = 7. LCM = 49 × 21 ÷ 7 = 147.
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 12 and 24.
- List factors of 12 and 24.
- The largest factor they share is 12.
- Answer: 12
Find the lowest common multiple (LCM) of 35 and 49.
- HCF(35, 49) = 7.
- LCM = 35 × 49 ÷ 7 = 245.
- Answer: 245
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 Introducing Scalar Multiples quiz really free?
- Yes. Every quizzes 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 quiz 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?
- Move on to Working with Scalar Multiples, Scalar Multiples in Context, Vector Notation, Adding Vectors, which build directly on this idea.
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