Free Grade 3 Working with Factors Worksheets
Free Grade 3 worksheets for Working with 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with factors
Identify working with factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with factors
Explain working with factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with factors
Calculate working with factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with factors
Compare working with 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 Working with 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 24.[1]
- 2.List all the factors of 36.[1]
- 3.List all the factors of 20.[1]
- 4.List all the factors of 12.[1]
- 5.Find the highest common factor (HCF) of 16 and 8.[2]
- 6.Find the highest common factor (HCF) of 45 and 54.[2]
- 7.Find the highest common factor (HCF) of 49 and 21.[2]
- 8.Find the highest common factor (HCF) of 28 and 8.[2]
- 9.Find the lowest common multiple (LCM) of 56 and 32.[3]
- 10.Find the lowest common multiple (LCM) of 15 and 21.[3]
- 11.Find the lowest common multiple (LCM) of 20 and 12.[3]
- 12.Find the lowest common multiple (LCM) of 10 and 35.[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, 9, 12, 18, 36
Find factor pairs that multiply to 36. 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6
3. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
4. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
5. 8
List factors of 16 and 8. The largest factor they share is 8.
6. 9
List factors of 45 and 54. The largest factor they share is 9.
7. 7
List factors of 49 and 21. The largest factor they share is 7.
8. 4
List factors of 28 and 8. The largest factor they share is 4.
9. 224
HCF(56, 32) = 8. LCM = 56 × 32 ÷ 8 = 224.
10. 105
HCF(15, 21) = 3. LCM = 15 × 21 ÷ 3 = 105.
11. 60
HCF(20, 12) = 4. LCM = 20 × 12 ÷ 4 = 60.
12. 70
HCF(10, 35) = 5. LCM = 10 × 35 ÷ 5 = 70.
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 63 and 45.
- List factors of 63 and 45.
- The largest factor they share is 9.
- Answer: 9
Find the lowest common multiple (LCM) of 14 and 49.
- HCF(14, 49) = 7.
- LCM = 14 × 49 ÷ 7 = 98.
- Answer: 98
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 Working with Factors
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Frequently asked
- Is this Grade 3 Working with Factors 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 Introducing Factors, Proportion. 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 Working with Factors?
- Move on to Factors in Context, Multiples, Prime Numbers, Prime Factorisation, which build directly on this idea.
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