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MathematicsMultiplication & DivisionAges 11–13

Factors, multiples, and primes (age 11+)

Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property

Lesson

Set out your lesson

Use prime products to explain HCF and LCM for positive whole numbers.

Before teaching

Use this short check, then start teaching.

Activity

Check that 6 divides 18 exactly and ask for the factor pairs of 12. Pause for factor-pair work if needed.

Policy

Check learner readiness separately; the existence of a prerequisite lesson is not evidence of attainment.

Printer, credit, and teaching notes

Check learner readiness separately; the existence of a prerequisite lesson is not evidence of attainment.

Use a pencil and supplied factor-work card. No prepared factor cards are needed.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras
Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

  • Canonical wording 'any integer' and 'every number' needs domain correction: this lesson restricts the theorem to positive integers greater than 1. The uniqueness theorem is explained, not proved.

Record actual responses, assistance and access mode; never invent observations or infer mastery.

Share teaching feedback

Continue learning
Share and support
Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

View learner plans ($12/mo per learner) See sample family archive

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

BBC Bitesize · Practice link — not the full lesson

KS3 Maths

Open practice (new tab)
Before you open · source notes

KS3 Maths supports Factors, multiples, and primes (age 11+). An adult previews and guides; this is a learning page, not a scored quiz.

Free educational page, no sign-in required for the tested path.

Before you open

Ask the learner one fact they learned and one question they still have.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public BBC Bitesize page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

BBC Bitesize. “KS3 Maths.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

  • Express any integer as a product of its prime factors using index notation
  • Find the HCF and LCM of two numbers using prime factorisation
  • Apply the unique factorisation theorem to explain why every number has exactly one set of prime factors
“Can your child find the highest common factor of two numbers like 24 and 36 — working out the biggest number that divides exactly into both — and explain how they found it?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Multiplication & Division
Age range
Ages 11–13

Standards

ccss-math:6.NS.4the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-B2.6uk-nc-2013:KS3.Maths.Num.3