1.2 Number properties including prime factor decomposition
Use factors, multiples, primes and prime decomposition to reveal number structure and solve HCF or LCM problems.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Recognise common number properties and use factor, multiple, prime, square and cube vocabulary.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Express integers as products of prime factors.
Exam cue: Translate the context into a factor or multiple condition, then justify the selected HCF or LCM.
Concept 3
Use prime decomposition to find highest common factors and least common multiples.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 1, Unit 2, Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Confusing a factor shared by two numbers with the least common multiple of those numbers.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Factor
A factor divides an integer exactly.
Multiple
A multiple is obtained by multiplying an integer by another integer.
Prime
A prime number has exactly two positive factors: one and itself.
HCF
The highest common factor is the greatest factor shared by the values.
LCM
The least common multiple is the smallest positive multiple shared by the values.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
What is the greatest number that divides both 84 and 126 exactly?
Find the smallest positive multiple shared by 18 and 24.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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