FinanceCalcs
Prime Factorization Calculator
Enter any number to see its prime factorization as a visual factor tree. Watch how every number breaks down into prime branches, step by step. Great for homework, fractions, and GCF/LCM problems.
Factor Tree
"Every whole number greater than 1 has exactly one prime factorization — no matter how you build the factor tree, you always end up with the same prime numbers at the bottom. This is called the Fundamental Theorem of Arithmetic."
How to build a factor tree
Step 1: Write the number at the top of your tree.
Step 2: Find any two factors that multiply to make it. Split the number into two branches. (Tip: always try dividing by 2 first, then 3, then 5…)
Step 3: If a branch is prime (circle it), it’s a leaf — stop there. If it’s not prime, split it again.
Step 4: Keep splitting until every branch ends in a prime number.
Step 5: Collect all the primes at the bottom — that’s your prime factorization!
Quick Questions
Does it matter which factors I pick first?
No! You can split a number any way you like and you’ll always get the same primes at the end. For example, 12 = 2 × 6 = 3 × 4. Both trees give you 2 × 2 × 3 at the bottom. This is the Fundamental Theorem of Arithmetic.
What is exponential notation?
When the same prime appears more than once, we use exponents to write it more neatly. Instead of 2 × 2 × 2 × 3, we write 2³ × 3. The small raised number (exponent) tells you how many times that prime is multiplied. 2³ means 2 × 2 × 2 = 8.
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