Free Grade 3 Factors and Multiples Lessons
Free Grade 3 lessons for Factors and 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain factors and multiples
Explain factors and multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factors and multiples
Calculate factors and multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factors and multiples
Compare factors and multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify factors and multiples
Justify factors and 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 Factors and 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 24.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 35 and 25.[2]
- 6.Find the highest common factor (HCF) of 12 and 12.[2]
- 7.Find the highest common factor (HCF) of 48 and 48.[2]
- 8.Find the highest common factor (HCF) of 18 and 18.[2]
- 9.Find the lowest common multiple (LCM) of 18 and 27.[3]
- 10.Find the lowest common multiple (LCM) of 12 and 6.[3]
- 11.Find the lowest common multiple (LCM) of 14 and 28.[3]
- 12.Find the highest common factor (HCF) of 35 and 35.[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, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 5
List factors of 35 and 25. The largest factor they share is 5.
6. 12
List factors of 12 and 12. The largest factor they share is 12.
7. 48
List factors of 48 and 48. The largest factor they share is 48.
8. 18
List factors of 18 and 18. The largest factor they share is 18.
9. 54
HCF(18, 27) = 9. LCM = 18 × 27 ÷ 9 = 54.
10. 12
HCF(12, 6) = 6. LCM = 12 × 6 ÷ 6 = 12.
11. 28
HCF(14, 28) = 14. LCM = 14 × 28 ÷ 14 = 28.
12. 35
List factors of 35 and 35. The largest factor they share is 35.
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 12 and 21.
- List factors of 12 and 21.
- The largest factor they share is 3.
- Answer: 3
Find the lowest common multiple (LCM) of 40 and 24.
- HCF(40, 24) = 8.
- LCM = 40 × 24 ÷ 8 = 120.
- Answer: 120
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 Factors and Multiples lesson really free?
- Yes. Every lessons 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 Proportion, Ratio. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Factors and Multiples?
- Move on to Powers and Roots, Algebra, Geometry, Measurement, which build directly on this idea.
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