Prime Factorization Calculator
Enter a whole number (2 or greater) to find its prime factorization.
How prime factorization works
Prime factorization breaks a number down into the prime numbers that multiply together to produce it. This calculator uses trial division, testing each number starting from 2 to see if it divides evenly, dividing it out when it does, and continuing until only prime factors remain.
Every whole number greater than 1 has exactly one prime factorization (ignoring the order of factors) — this is known as the Fundamental Theorem of Arithmetic. Factors that repeat are shown with an exponent, like 2³ for 2 × 2 × 2.
Frequently asked questions
What is a prime number?
A prime number is a whole number greater than 1 that has no positive divisors other than 1 and itself — examples include 2, 3, 5, 7, 11, and 13.
What does it mean if a number has only one prime factor?
If the factorization shows just one prime (with no exponent, or itself raised to the first power), the number you entered is prime.
Why does factorization only test up to the square root of the number?
If a number n has a factor larger than its square root, it must also have a corresponding factor smaller than the square root — so checking divisors up to √n is enough to find every prime factor.