Every whole number greater than 1 can be written as a product of prime factors. Prime factors are prime numbers that multiply together to make the original number.

To find the prime factorisation of a number, divide it repeatedly by prime numbers until only primes remain.

When a prime factor appears more than once, it can be written using index form (powers).

For example, the prime factorisation of 12 is:

$$
12 = 2 \times 2 \times 3
$$

This can be written in index form as:

$$
12 = 2^2 \times 3
$$

Another example is 60:

$$
60 = 2 \times 2 \times 3 \times 5
$$

Written in index form:

$$
60 = 2^2 \times 3 \times 5
$$

You should be able to:

• Identify the prime factors of a number
• Write repeated factors using index notation
• Express numbers fully as a product of prime factors in index form

Prime factorisation is an important foundation for working with fractions, highest common factors, and lowest common multiples.