Prime factor decomposition

Tier: #Foundation #Higher

🔗What you need to know first
How to

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.

Questions to practise

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📝Past paper questions
💬What the examiners say
  • "The most common error leading to zero marks was an incomplete factor tree where a branch ended with a composite number rather than a prime."
  • "For finding HCF, using prime factors and Venn diagrams was the most successful approach — students who listed factors manually often missed some."
⬆️How you can quickly improve
  • After completing a factor tree, check every endpoint — if it has factors other than 1 and itself, keep splitting.
  • Write the final answer using × between factors: 2 × 2 × 31, not a list with commas.
  • Label at the top of your working whether you're finding HCF or LCM, and write the rule for each: HCF uses lowest powers, LCM uses highest.
💡Watch
🔓What this unlocks
ℹ️Calculator tricks

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 $2^3\times3\times5$