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
Share and support
Teaching Table
Set out your lesson
Use prime products to explain HCF and LCM for positive whole numbers.
Check that 6 divides 18 exactly and ask for the factor pairs of 12. Pause for factor-pair work if needed.
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.
Record actual responses, assistance and access mode; never invent observations or infer mastery.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
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.
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.
Learning resources
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
No reviewed resources for this concept yet.
The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
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 11–12
Standards