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Free Grade 3 Introducing HCF Worksheets

Free Grade 3 worksheets for Introducing HCF: 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.

Price

Free

Difficulty

Higher

Estimated time

20 min

Total marks

24

Learning objectives

Every objective is checkable, and each one maps to an activity and an assessment.

  • RememberIdentify introducing hcf

    Identify introducing hcf accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • UnderstandExplain introducing hcf

    Explain introducing hcf accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • ApplyCalculate introducing hcf

    Calculate introducing hcf accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • AnalyseCompare introducing hcf

    Compare introducing hcf 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.

Prime Factorisation

How Introducing HCF 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.

Key wordsfactormultipleprimeHCFLCM

12 practice questions

Easy to hard, 24 marks in total. Try them first, then open the answers.

  1. 1.List all the factors of 24.[1]
  2. 2.List all the factors of 40.[1]
  3. 3.List all the factors of 20.[1]
  4. 4.List all the factors of 30.[1]
  5. 5.Find the highest common factor (HCF) of 18 and 6.[2]
  6. 6.Find the highest common factor (HCF) of 28 and 8.[2]
  7. 7.Find the highest common factor (HCF) of 35 and 35.[2]
  8. 8.Find the highest common factor (HCF) of 56 and 32.[2]
  9. 9.Find the highest common factor (HCF) of 9 and 9.[3]
  10. 10.Find the lowest common multiple (LCM) of 18 and 27.[3]
  11. 11.Find the lowest common multiple (LCM) of 12 and 14.[3]
  12. 12.Find the highest common factor (HCF) of 32 and 32.[3]
Show answers and working

  1. 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. 2. 1, 2, 4, 5, 8, 10, 20, 40

    Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8

  3. 3. 1, 2, 4, 5, 10, 20

    Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5

  4. 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. 5. 6

    List factors of 18 and 6. The largest factor they share is 6.

  6. 6. 4

    List factors of 28 and 8. The largest factor they share is 4.

  7. 7. 35

    List factors of 35 and 35. The largest factor they share is 35.

  8. 8. 8

    List factors of 56 and 32. The largest factor they share is 8.

  9. 9. 9

    List factors of 9 and 9. The largest factor they share is 9.

  10. 10. 54

    HCF(18, 27) = 9. LCM = 18 × 27 ÷ 9 = 54.

  11. 11. 84

    HCF(12, 14) = 2. LCM = 12 × 14 ÷ 2 = 84.

  12. 12. 32

    List factors of 32 and 32. The largest factor they share is 32.

Worked examples

Easy example

List all the factors of 18.

  1. Find factor pairs that multiply to 18.
  2. 1 × 18
  3. 2 × 9
  4. 3 × 6
  5. Answer: 1, 2, 3, 6, 9, 18
Medium example

Find the highest common factor (HCF) of 12 and 15.

  1. List factors of 12 and 15.
  2. The largest factor they share is 3.
  3. Answer: 3
Hard example

Find the lowest common multiple (LCM) of 18 and 24.

  1. HCF(18, 24) = 6.
  2. LCM = 18 × 24 ÷ 6 = 72.
  3. Answer: 72

Interactive practice

Free, no account required — answer on screen or print it.

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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.

CAMBRIDGE CAM-120.1 — Mapped statement covering Introducing HCF.NATIONAL-CURRICULUM NAT-260.2 — Mapped statement covering Introducing HCF.

Every free resource for Introducing HCF

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Free Introducing HCF quizzes
Free Introducing HCF flashcards
Free Introducing HCF lessons
Free Introducing HCF lesson plans

Goes deeper

The entities below this one, each with the same complete free resource set.

Introducing HCF Essentials
Introducing HCF Techniques
Introducing HCF Word Problems
Introducing HCF Common Errors

Sibling concepts

Working with HCF
HCF in Context

Related concepts

Lateral links, including across subjects.

Working with HCF
HCF in Context
Factors

Next topics

Working with HCF
HCF in Context
Factors
Multiples

All free formats for this concept

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Frequently asked

Is this Grade 3 Introducing HCF 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 Prime Factorisation. 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 Introducing HCF?
Move on to Working with HCF, HCF in Context, Factors, Multiples, which build directly on this idea.

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