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GCSE Mathematics · key term
The greatest whole number that divides exactly into each of two or more numbers.
Used by AQA, Edexcel and OCR
Specification N4, R3 · Paper 1, Paper 2, Paper 3
The greatest positive whole number that divides each of the given numbers exactly.
Revise: Primes, Factors, and MultiplesThis is why the HCF uses the shared minimum powers, whereas the LCM uses the combined maximum powers.
For an HCF, use only primes shared by all the numbers and take their lowest powers. For an LCM, include every prime needed and take its highest power.
Check that an HCF divides each original number and that an LCM is a multiple of each original number.
In a context question, decide whether you need the largest equal grouping (HCF) or the first time repeating events coincide (LCM).
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Specification N4, R3, R4 · Paper 1, Paper 2, Paper 3
The greatest positive integer that is a factor of each of the given numbers.
Revise: Primes, Factors and MultiplesIt gives a reliable way to compare the factor structure of two numbers and hence find their HCF and LCM.
The greatest whole number that divides exactly into every number being considered.
Specification 1.02c, 5.01a, 6.01e · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
The greatest whole number that is a factor of each of the given numbers.
Revise: HCF and LCMThis distinction is the foundation of HCF and LCM.
The greatest numerical and algebraic factor shared by every term in an expression.