Guides
A factor tree breaks a number into smaller factors again and again until only primes remain. It is the most visual way to find a prime factorization, and it always gives the same answer no matter where you start.
Build one for any number in the Prime Factorization Calculator, which draws the tree for you.
What is a factor tree?
Start with your number and split it into any two factors. Keep splitting each composite branch until every leaf is a prime. Those primes, multiplied together, equal the original number.
Step-by-step example: 60
60 → 6 × 10. Then 6 → 2 × 3 and 10 → 2 × 5. The leaves are 2, 3, 2, 5, so 60 = 2 × 2 × 3 × 5.
Writing the answer in exponent form
Group repeated primes as powers: 60 = 2² × 3 × 5. This canonical form is what most calculators and textbooks expect.
Why the answer is always the same
The Fundamental Theorem of Arithmetic guarantees every number above 1 has exactly one prime factorization — so starting 60 → 4 × 15 leads to the same 2² × 3 × 5.
Tips for big numbers
Pull out the smallest prime first (2, then 3, then 5…). Use divisibility rules to spot factors quickly. For very large numbers, the calculator uses fast trial division and shows the tree and divisor list together.
Key takeaways
- A factor tree splits a number until only primes remain.
- Group repeats as powers for the canonical form.
- The result is unique regardless of starting split.
- Pull out the smallest prime first.
Prime Factorization Calculator
Break any number into primes with an animated factor tree and divisor list.
Open the Prime Factorization CalculatorFrequently asked questions
What is the factor tree method?
A way to find the prime factors of a number by repeatedly splitting it into smaller factors until only primes remain.
Does it matter how I split the number first?
No. By the Fundamental Theorem of Arithmetic, every starting split leads to the same set of prime factors.
How do I write the final answer?
Group repeated primes as powers, e.g. 60 = 2² × 3 × 5 (canonical form).
The LCM Calculator Team
Math educators and engineers building free, accurate calculators with step-by-step solutions, visual diagrams and AI insights.
Keep reading