Prime Factors, HCF & LCMEdexcel GCSE Maths: Flashcards

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What is a prime number?

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What is a prime number?: A number greater than 1 with exactly two factors: 1 and itself.
Is 1 a prime number?: No — 1 has only one factor, itself, so it does not meet the definition of prime.
What is the only even prime number?: 2
What is a factor of a number?: A whole number that divides exactly into it with no remainder.
What is prime factorisation?: Expressing a number as a product of its prime factors, usually in index form.
Find the prime factorisation of 60.: 2² × 3 × 5
What does HCF stand for and mean?: Highest Common Factor — the largest number that divides exactly into two or more numbers.
What does LCM stand for and mean?: Lowest Common Multiple — the smallest number that is a multiple of two or more numbers.
How do you find the HCF from two prime factorisations?: Multiply the lowest power of each prime factor common to both numbers.
How do you find the LCM from two prime factorisations?: Multiply the highest power of every prime factor that appears in either number.
Find the HCF of 12 (2²×3) and 18 (2×3²).: 6 (2¹ × 3¹, the lowest powers of the shared primes).
Find the LCM of 12 (2²×3) and 18 (2×3²).: 36 (2² × 3², the highest powers of all primes involved).
In a Venn diagram of prime factors, what does the overlap represent?: The HCF — the product of the common prime factors.
In a Venn diagram of prime factors, what does the product of everything represent?: The LCM — the product of all the prime factors in every region.
What method is used to break a number into its prime factors step by step?: A factor tree — repeatedly splitting into factors until each branch ends in a prime number.