Prime Number definition
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. For example, 7 is a prime number because the only whole numbers that divide exactly into 7 are 1 and 7. The number 10 is not prime because it has more than two factors: 1, 2, 5 and 10. Numbers greater than 1 that are not prime are called composite numbers.
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and 23. The number 2 is the only even prime number because it has exactly two factors, 1 and 2. Every other even number can be divided by 2 as well as 1 and itself, so it has more than two factors. This makes 2 a special prime number.
Prime numbers are used in number, factors, multiples, divisibility, fractions, highest common factor, lowest common multiple, square numbers and problem solving. At GCSE level, students use prime numbers in prime factorisation, factor trees, HCF and LCM questions. Prime numbers also appear in more advanced maths, computer science, coding, cryptography and number theory.
A common question is whether 1 is a prime number. The answer is no. A prime number must have exactly two factors, but 1 has only one factor, which is itself. This definition is important because it makes prime factorisation work properly. If 1 were counted as prime, the same number could have many different prime factorisations, making the system less clear.
Prime factorisation means writing a number as a product of prime numbers. For example, 60 can be written as 2 times 2 times 3 times 5. These are all prime factors. A factor tree can help break a number down step by step until only prime numbers remain. This method is useful for simplifying fractions and finding HCF or LCM.
To test whether a number is prime, check whether it has factors other than 1 and itself. For smaller numbers, divisibility rules can help. For example, a number ending in 0, 2, 4, 6 or 8 is divisible by 2, so it is not prime unless it is 2 itself. A number with digits adding to a multiple of 3 is divisible by 3. These checks quickly rule out many composite numbers.
Prime numbers are important because they are like the building blocks of whole numbers. Every whole number greater than 1 is either prime or can be made by multiplying prime numbers together. This is why prime factorisation is so useful. It reveals the hidden structure of a number and makes many number problems easier to organise.
Related ideas include factors, multiples, composite numbers, prime factors, factor trees, divisibility, highest common factor and lowest common multiple. A clear definition of prime number helps students understand why some numbers cannot be broken down further using whole-number factors. In exams, remember that a prime number must be greater than 1 and must have exactly two factors.