Factor Trees – A Visual Way to Find Prime Factors

A factor tree is a diagram that breaks a number down into its prime factors step by step. Each branch splits a number into two factors, and branching continues until every tip of the tree is a prime number.

Factor trees are a relatively modern teaching invention, popularised in maths classrooms through the twentieth century as a visual, intuitive alternative to purely written methods like the ladder. They are also a specific example of a much bigger idea in computer science: a “tree” data structure, where each item branches into smaller sub-items until you reach the simplest possible pieces. Search engines, file systems, and decision-making algorithms all rely on exactly this branch-until-you-can’t-branch-further logic.

How to Draw a Factor Tree

Write the starting number at the top.
Choose any pair of factors that multiply to give it (not 1 and the number itself).
Write each factor as a branch below.
If a factor is composite, split it again. If it is prime, circle it — that branch is complete.
Collect all circled primes. That is the prime factorization.

Press each step below to build a real factor tree for 60, one split at a time, and watch the prime factorization grow to match.

Composite (splits again)

Prime (branch ends)

Circled in final answer

60 = ?

Click Step 1 or Auto Play to begin!

60 = 2² × 3 × 5
Every branch ended in a prime — multiply them back together (2×2×3×5) and you get 60 again.

Example 1 – Factor Tree for 48

48 splits to 6 × 8. 6 → 2 × 3 (both prime). 8 → 2 × 4 → 4 splits to 2 × 2. Primes: 2, 3, 2, 2, 2 → 48 = 2⁴ × 3

Example 2 – Factor Tree for 180

180 → 9 × 20 → 9 = 3 × 3; 20 → 4 × 5 → 4 = 2 × 2. Primes: 3, 3, 2, 2, 5 → 180 = 2² × 3² × 5

Different Trees, Same Answer

You can start by splitting in different ways and still get the same answer. That is the power of the Fundamental Theorem of Arithmetic.

Factor tree for 24 — two starting splits

Split A: 24 = 4 × 6 → 2×2 × 2×3 = 2³ × 3

Split B: 24 = 3 × 8 → 3 × 2×4 → 3 × 2 × 2×2 = 2³ × 3

Same result: 2³ × 3

Tips for Accuracy

Always try to spot an even factor first — dividing by 2 is easiest.
Circle primes as you go so you don't lose track.
Count the prime branches at the end to double-check by multiplying back up.

Key Takeaways

Any starting split works — the final prime factorization is always the same.
A branch ends only when the tip is a prime number.
Multiply all the circled primes to verify you get the original number back.

Practice: Factor Trees

Factor Tree Question