Free Grade 3 Factors Lessons
Free Grade 3 lessons for Factors: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify factors
Identify factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain factors
Explain factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factors
Calculate factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factors
Compare factors 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 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 28.[1]
- 3.List all the factors of 24.[1]
- 4.List all the factors of 30.[1]
- 5.Find the highest common factor (HCF) of 32 and 32.[2]
- 6.Find the highest common factor (HCF) of 45 and 36.[2]
- 7.Find the highest common factor (HCF) of 20 and 8.[2]
- 8.Find the highest common factor (HCF) of 49 and 42.[2]
- 9.Find the highest common factor (HCF) of 15 and 15.[3]
- 10.Find the lowest common multiple (LCM) of 32 and 48.[3]
- 11.Find the lowest common multiple (LCM) of 18 and 6.[3]
- 12.Find the highest common factor (HCF) of 24 and 24.[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, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
3. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
4. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
5. 32
List factors of 32 and 32. The largest factor they share is 32.
6. 9
List factors of 45 and 36. The largest factor they share is 9.
7. 4
List factors of 20 and 8. The largest factor they share is 4.
8. 7
List factors of 49 and 42. The largest factor they share is 7.
9. 15
List factors of 15 and 15. The largest factor they share is 15.
10. 96
HCF(32, 48) = 16. LCM = 32 × 48 ÷ 16 = 96.
11. 18
HCF(18, 6) = 6. LCM = 18 × 6 ÷ 6 = 18.
12. 24
List factors of 24 and 24. The largest factor they share is 24.
Worked examples
List all the factors of 36.
- Find factor pairs that multiply to 36.
- 1 × 36
- 2 × 18
- 3 × 12
- 4 × 9
- 6 × 6
- Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Find the highest common factor (HCF) of 18 and 36.
- List factors of 18 and 36.
- The largest factor they share is 18.
- Answer: 18
Find the lowest common multiple (LCM) of 9 and 21.
- HCF(9, 21) = 3.
- LCM = 9 × 21 ÷ 3 = 63.
- Answer: 63
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 Factors
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Factors 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. 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?
- Move on to Multiples, Prime Numbers, Prime Factorisation, HCF, which build directly on this idea.
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