Break any integer into its prime building blocks instantly
Input
Enter any positive integer up to 1,000,000,000.
Try an example
Result
Prime factors
Step-by-step division
All divisors (24)
What is Prime Factorization?
Every integer greater than 1 can be written as a unique product of prime numbers — this is the Fundamental Theorem of Arithmetic. The prime factorization expresses a number in exponential form showing which primes are multiplied, and how many times each appears.
The prime factorization calculator breaks any positive integer into its unique product of prime numbers — shown in exponential form with exponents. Grounded in the Fundamental Theorem of Arithmetic, it reveals the hidden prime structure of any number, displays a step-by-step division ladder, lists all divisors, and counts distinct prime factors. Ideal for students, teachers, and anyone working with number theory.
Prime factorization expresses a number as a product of prime numbers. For example, 360 = 2³ × 3² × 5. Every integer greater than 1 has exactly one prime factorization — a fact known as the Fundamental Theorem of Arithmetic.
If you enter a prime number such as 97, the calculator recognizes it immediately and labels it as prime. A prime has no smaller divisors, so it is its own prime factorization.
This tool supports integers up to 1,000,000,000 (one billion). For numbers in that range the trial division algorithm is fast enough to run in the browser without any noticeable delay.
If a number has prime factorization p₁^a × p₂^b × …, then the total count of divisors is (a+1)(b+1)…. For example, 12 = 2² × 3 has (2+1)(1+1) = 6 divisors: 1, 2, 3, 4, 6, 12.