#### Tier: #Foundation #Higher
A question will nearly always be written in the following way: Express 100 as a product of its prime factors
This topic involves breaking down (decomposing) numbers into their prime factor products. For example, $100 = 2^{2}\times5^2$
Once you have all of the prime factors, you multiply them to give the final answer: $$100 = 2\times2\times5\times5$$
Because there are duplicates, we collect them together as indices: $$100 = 2^{2}\times5^2$$ A very common error is for students to write the answer as 2, 2, 5, 5. If you check the question again, it asks for the product which means multiply.
New to Bow Tie Maths? It generates questions on this topic, marks them instantly, and tracks what you've mastered. Free to sign up.
Your calculator has a FACT button which will take any number and decompose it into its prime factors Try typing 120 into your calculator then press the equals button Then press Shift and FACT. The calculator will show $2^3\times3\times5$
2025 Jun 2H GCSE Q1 (2 marks) 2024 Jun 2H GCSE Q2 (2 marks) 2023 Jun 2H GCSE Q2 (2 marks) 2022 Jun 1H GCSE Q2 (2 marks) 2019 Nov 1H GCSE Q1 (1 mark) 2017 Nov 1H GCSE Q1 (2 marks) 2017 Jun 1H GCSE Q2 (2 marks)