Free Grade 3 Working with Factorising Quizzes
Free Grade 3 quizzes for Working with Factorising: 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.
- RememberIdentify working with factorising
Identify working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with factorising
Explain working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with factorising
Calculate working with factorising accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with factorising
Compare working with factorising 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 Factorising 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 18.[1]
- 2.List all the factors of 28.[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 10 and 25.[2]
- 6.Find the highest common factor (HCF) of 35 and 25.[2]
- 7.Find the highest common factor (HCF) of 28 and 14.[2]
- 8.Find the highest common factor (HCF) of 15 and 20.[2]
- 9.Find the lowest common multiple (LCM) of 25 and 35.[3]
- 10.Find the lowest common multiple (LCM) of 10 and 12.[3]
- 11.Find the lowest common multiple (LCM) of 36 and 18.[3]
- 12.Find the highest common factor (HCF) of 4 and 4.[3]
Show answers and working
1. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
2. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
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. 5
List factors of 10 and 25. The largest factor they share is 5.
6. 5
List factors of 35 and 25. The largest factor they share is 5.
7. 14
List factors of 28 and 14. The largest factor they share is 14.
8. 5
List factors of 15 and 20. The largest factor they share is 5.
9. 175
HCF(25, 35) = 5. LCM = 25 × 35 ÷ 5 = 175.
10. 60
HCF(10, 12) = 2. LCM = 10 × 12 ÷ 2 = 60.
11. 36
HCF(36, 18) = 18. LCM = 36 × 18 ÷ 18 = 36.
12. 4
List factors of 4 and 4. The largest factor they share is 4.
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 56 and 24.
- List factors of 56 and 24.
- The largest factor they share is 8.
- Answer: 8
Find the highest common factor (HCF) of 27 and 27.
- List factors of 27 and 27.
- The largest factor they share is 27.
- Answer: 27
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 Factorising
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 Factorising quiz really free?
- Yes. Every quizzes 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 Factorising, Expanding Brackets. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Factorising?
- Move on to Factorising in Context, Using Letters for Numbers, Collecting Like Terms, Substitution, which build directly on this idea.
Related resources
Stuck on Working with Factorising? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor