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Highest Common Factor Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Highest Common Factor (HCF)
The largest number that divides exactly into two or more numbers.
How to find the HCF using listing
List all the factors of each number and identify the largest factor that appears in all lists.
How to find the HCF using prime factorisation
Write each number as a product of prime factors, then multiply the common prime factors.
Prime factorisation
Breaking a number down into a product of prime numbers, often shown using a factor tree.
HCF of 12 and 18 (listing method)
Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. HCF = 6.
HCF of 24 and 36 (prime factorisation)
24 = 2³ × 3, 36 = 2² × 3². Common factors: 2² × 3 = 12. HCF = 12.
HCF of 15 and 20 (listing method)
Factors of 15: 1, 3, 5, 15. Factors of 20: 1, 2, 4, 5, 10, 20. HCF = 5.
HCF of 28 and 42 (prime factorisation)
28 = 2² × 7, 42 = 2 × 3 × 7. Common factors: 2 × 7 = 14. HCF = 14.
Why is the HCF useful?
The HCF is used to simplify fractions and solve problems involving shared factors.
Difference between HCF and LCM
HCF is the largest common factor of two numbers, while LCM is the smallest number divisible by both.
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