Factors, Multiples and Primes

This lesson covers factors, multiples, prime numbers, prime factorisation, and finding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). These are fundamental Number topics in the Edexcel GCSE Mathematics (1MA1) specification, tested on all tiers and frequently appearing on Paper 1 (non-calculator).

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Key Vocabulary

Term	Meaning
Factor	A number that divides exactly into another number
Multiple	The result of multiplying a number by an integer
Prime number	A number with exactly two factors: 1 and itself
Composite number	A number with more than two factors
Prime factor	A factor that is a prime number
Prime factorisation	Writing a number as a product of its prime factors
HCF	Highest Common Factor — the largest factor shared by two or more numbers
LCM	Lowest Common Multiple — the smallest multiple shared by two or more numbers

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Factors

The factors of a number are all the whole numbers that divide into it exactly.

Worked Example 1

Find all the factors of 36.