Free Grade 3 Working with Factors Lessons
Free Grade 3 lessons 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
15 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 36.[1]
- 2.List all the factors of 12.[1]
- 3.List all the factors of 40.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 36 and 45.[2]
- 6.Find the highest common factor (HCF) of 42 and 21.[2]
- 7.Find the highest common factor (HCF) of 28 and 28.[2]
- 8.Find the highest common factor (HCF) of 20 and 20.[2]
- 9.Find the lowest common multiple (LCM) of 45 and 18.[3]
- 10.Find the highest common factor (HCF) of 35 and 35.[3]
- 11.Find the lowest common multiple (LCM) of 35 and 25.[3]
- 12.Find the highest common factor (HCF) of 49 and 49.[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, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
3. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
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. 9
List factors of 36 and 45. The largest factor they share is 9.
6. 21
List factors of 42 and 21. The largest factor they share is 21.
7. 28
List factors of 28 and 28. The largest factor they share is 28.
8. 20
List factors of 20 and 20. The largest factor they share is 20.
9. 90
HCF(45, 18) = 9. LCM = 45 × 18 ÷ 9 = 90.
10. 35
List factors of 35 and 35. The largest factor they share is 35.
11. 175
HCF(35, 25) = 5. LCM = 35 × 25 ÷ 5 = 175.
12. 49
List factors of 49 and 49. The largest factor they share is 49.
Worked examples
List all the factors of 28.
- Find factor pairs that multiply to 28.
- 1 × 28
- 2 × 14
- 4 × 7
- Answer: 1, 2, 4, 7, 14, 28
Find the highest common factor (HCF) of 48 and 40.
- List factors of 48 and 40.
- The largest factor they share is 8.
- Answer: 8
Find the highest common factor (HCF) of 12 and 12.
- List factors of 12 and 12.
- The largest factor they share is 12.
- Answer: 12
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
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with 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 Introducing Factors, 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 Working with Factors?
- Move on to Factors in Context, Multiples, Prime Numbers, Prime Factorisation, which build directly on this idea.
Related resources
Stuck on Working with Factors? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor