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Free Grade 3 Introducing HCF Lessons

Free Grade 3 lessons 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

25 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 28.[1]
  2. 2.List all the factors of 12.[1]
  3. 3.List all the factors of 18.[1]
  4. 4.List all the factors of 24.[1]
  5. 5.Find the highest common factor (HCF) of 12 and 12.[2]
  6. 6.Find the highest common factor (HCF) of 32 and 16.[2]
  7. 7.Find the highest common factor (HCF) of 63 and 18.[2]
  8. 8.Find the highest common factor (HCF) of 16 and 24.[2]
  9. 9.Find the lowest common multiple (LCM) of 6 and 18.[3]
  10. 10.Find the lowest common multiple (LCM) of 30 and 18.[3]
  11. 11.Find the lowest common multiple (LCM) of 8 and 16.[3]
  12. 12.Find the lowest common multiple (LCM) of 16 and 24.[3]
Show answers and working

  1. 1. 1, 2, 4, 7, 14, 28

    Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7

  2. 2. 1, 2, 3, 4, 6, 12

    Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4

  3. 3. 1, 2, 3, 6, 9, 18

    Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6

  4. 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. 12

    List factors of 12 and 12. The largest factor they share is 12.

  6. 6. 16

    List factors of 32 and 16. The largest factor they share is 16.

  7. 7. 9

    List factors of 63 and 18. The largest factor they share is 9.

  8. 8. 8

    List factors of 16 and 24. The largest factor they share is 8.

  9. 9. 18

    HCF(6, 18) = 6. LCM = 6 × 18 ÷ 6 = 18.

  10. 10. 90

    HCF(30, 18) = 6. LCM = 30 × 18 ÷ 6 = 90.

  11. 11. 16

    HCF(8, 16) = 8. LCM = 8 × 16 ÷ 8 = 16.

  12. 12. 48

    HCF(16, 24) = 8. LCM = 16 × 24 ÷ 8 = 48.

Worked examples

Easy example

List all the factors of 20.

  1. Find factor pairs that multiply to 20.
  2. 1 × 20
  3. 2 × 10
  4. 4 × 5
  5. Answer: 1, 2, 4, 5, 10, 20
Medium example

Find the highest common factor (HCF) of 18 and 27.

  1. List factors of 18 and 27.
  2. The largest factor they share is 9.
  3. Answer: 9
Hard example

Find the lowest common multiple (LCM) of 42 and 21.

  1. HCF(42, 21) = 21.
  2. LCM = 42 × 21 ÷ 21 = 42.
  3. Answer: 42

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 worksheets
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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

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Frequently asked

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

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