Prime Factors, HCF & LCMEdexcel IGCSE Maths: Flashcards

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What is a prime number?

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What is a prime number?: A whole number greater than 1 with exactly two factors: 1 and itself.
Define prime factorisation.: Writing a number as a product of prime numbers only, e.g. $360 = 2^{3} \times 3^{2} \times 5$ .
What is the HCF of two numbers?: The largest whole number that divides exactly into both numbers.
What is the LCM of two numbers?: The smallest whole number that both original numbers divide into exactly.
Explain how to find the HCF from two prime factorisations.: For each prime common to both numbers, take the lowest power it appears with, then multiply these together.
Explain how to find the LCM from two prime factorisations.: For each prime appearing in either number, take the highest power it appears with, then multiply these together.
State the relationship linking HCF, LCM, $a$ and $b$ .: $\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b$
Name the diagram method used to find prime factors visually.: A factor tree — repeatedly split into factors until every branch ends in a prime.
Write $84$ as a product of its prime factors.: $84 = 2^{2} \times 3 \times 7$
Find the HCF of $84$ ( $2^{2} \times 3 \times 7$ ) and $126$ ( $2 \times 3^{2} \times 7$ ).: $2 \times 3 \times 7 = 42$
Find the LCM of $84$ ( $2^{2} \times 3 \times 7$ ) and $126$ ( $2 \times 3^{2} \times 7$ ).: $2^{2} \times 3^{2} \times 7 = 252$
What type of exam question usually needs the HCF?: Sharing/grouping items into the largest possible equal groups with nothing left over.
What type of exam question usually needs the LCM?: Finding when repeating events (e.g. buses, flashing lights) next happen at the same time.
What is the prime factorisation of a prime number itself, e.g. 13?: Just itself to the power 1: $13 = 13^{1}$ .