Free Grade 3 Introducing Multiples Essentials Worksheets
Free Grade 3 worksheets for Introducing 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing multiples essentials
Explain introducing multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing multiples essentials
Calculate introducing multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing multiples essentials
Compare introducing multiples essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing multiples essentials
Justify introducing 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 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 36.[1]
- 2.List all the factors of 20.[1]
- 3.List all the factors of 28.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 12 and 28.[2]
- 6.Find the highest common factor (HCF) of 16 and 24.[2]
- 7.Find the highest common factor (HCF) of 18 and 45.[2]
- 8.Find the highest common factor (HCF) of 9 and 6.[2]
- 9.Find the lowest common multiple (LCM) of 10 and 8.[3]
- 10.Find the lowest common multiple (LCM) of 18 and 36.[3]
- 11.Find the lowest common multiple (LCM) of 54 and 36.[3]
- 12.Find the lowest common multiple (LCM) of 9 and 6.[3]
Show answers and working
1. 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
2. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
3. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
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. 4
List factors of 12 and 28. The largest factor they share is 4.
6. 8
List factors of 16 and 24. The largest factor they share is 8.
7. 9
List factors of 18 and 45. The largest factor they share is 9.
8. 3
List factors of 9 and 6. The largest factor they share is 3.
9. 40
HCF(10, 8) = 2. LCM = 10 × 8 ÷ 2 = 40.
10. 36
HCF(18, 36) = 18. LCM = 18 × 36 ÷ 18 = 36.
11. 108
HCF(54, 36) = 18. LCM = 54 × 36 ÷ 18 = 108.
12. 18
HCF(9, 6) = 3. LCM = 9 × 6 ÷ 3 = 18.
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 21 and 6.
- List factors of 21 and 6.
- The largest factor they share is 3.
- Answer: 3
Find the lowest common multiple (LCM) of 14 and 12.
- HCF(14, 12) = 2.
- LCM = 14 × 12 ÷ 2 = 84.
- Answer: 84
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 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 Factors. 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 Multiples Essentials?
- Move on to Introducing Multiples Techniques, Introducing Multiples Word Problems, Introducing Multiples Common Errors, Working with Multiples, which build directly on this idea.
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