Prime numbers and prime factorisation

What is a prime number?

A prime number is a whole number greater than 1 that has exactly two divisors: 1 and itself. The first prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19...

Note: 1 is not a prime number (it has only one divisor, itself). 2 is the only even prime number.

What is a composite number?

A number greater than 1 that is not prime is called a composite number: it has at least one divisor other than 1 and itself. Example: 12 is composite because it is divisible by 2, 3, 4 and 6.

Factoring a number into prime factors

Any integer greater than 1 can be written as a product of prime numbers. To factor 60:

• 60 = 2 × 30
• 30 = 2 × 15
• 15 = 3 × 5

Therefore, 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

Step-by-step method

1. Divide the number by the smallest possible prime number (2, then 3, then 5...)
2. Repeat the process with the quotient obtained
3. Stop when the quotient is a prime number
4. Write down the product of all the prime factors found

Common pitfall

Don’t forget to repeat the same prime factor as many times as necessary. For example, for 8: 8 = 2 × 4 = 2 × 2 × 2 = 2³. Writing only ‘8 = 2 × 4’ is not a prime factorisation, as 4 is not a prime number.