# Prime factors

factors are of a number that are, themselves, prime numbers.

There are many methods to find the prime factors of a number, but one of the most common is to use a prime factor tree.

### Example

Write 40 as a of its prime factors.

Firstly, find two numbers that will multiply together to give 40. For example $$4 \times 10 = 40$$ would be one way of doing this calculation. Every has a unique prime factorisation, so it doesn’t matter which factors are chosen to start the factor tree as you will end up with the same answer.

Neither 4 nor 10 is a prime number, and this question is looking for prime factors, so each number must be broken down again into . Continue breaking down the factors into factor pairs until you are only left with prime numbers. Then circle these prime numbers.

The question has asked for a product of prime factors. Write all of the circled prime numbers (found in the prime factor tree) as a product.

This gives $$2 \times 2 \times 2 \times 5$$. This can be written in index form as $$2^3 \times 5$$.

This answer can be checked by making sure $$2 \times 2 \times 2 \times 5$$ is equal to 40. $$2 \times 2 \times 2 \times 5 = 40$$, so this answer is correct. The final answer is $$2^3 \times 5$$.

Question

Express 24 as a product of prime factors.

Here is one way to break down 24 into prime factors:

Now write 24 as a product of the circled prime numbers, $$2 \times 2 \times 2 \times 3 = 2^3 \times 3$$. As a check, work out $$2 \times 2 \times 2 \times 3$$ to make sure it gives an answer of 24.