Prime factors

Prime factors are factors 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.


Write 40 as a product 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 integer 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 factor pairs. Continue breaking down the factors into factor pairs until you are only left with prime numbers. Then circle these prime numbers.

Factors of the number 40

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 \(2^3 \times 5\).


Express 24 as a product of prime factors.

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

Factors of the number 24

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.