Prime factor trees
Objective. Express whole numbers as products of prime factors.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A prime factor tree breaks a whole number down step by step into the prime numbers that multiply together to make it. You start by splitting the number into any two factors, then keep splitting composite branches until every branch ends in a prime. For example, 60 splits into 6×10, then 6 splits into 2×3 and 10 splits into 2×5, giving 60=2×2×3×5. Writing the result using index notation, such as 2²×3×5, makes the answer tidy. However you split the number first, the final list of prime factors is always the same.
Worked example
Draw a prime factor tree for 72 and write 72 as a product of its prime factors.
- 1Split 72 into 8×9.
- 2Split 8 into 2×2×2, and split 9 into 3×3.
- 3Collect all the prime branches: 2, 2, 2, 3, 3.
- 4Write as a product: 2³×3².
Answer: 72 = 2³×3²
Concept mastery
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Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes stop a branch too early, leaving a composite number like 4 in the final list instead of splitting it into 2×2. Always check every end of the tree is a prime number.
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