What is the Factorization Calculator?
Factor any whole number into its prime factors with this free online factorization calculator. Enter a positive integer and get the prime factorization in exponential, expanded, or equation form, a full list of divisors when practical, divisor count, and step-by-step trial division. Runs entirely in your browser with no signup.
How to use the Factorization Calculator
- Enter a positive integer (2 or greater).
- Choose a display format: exponential, expanded, or equation.
- Click Factorize to see prime factors and divisors.
- Review the trial-division steps and prime breakdown.
- Copy the factorization or the full summary.
Common use cases
- Factoring 84 into 2² × 3 × 7 for homework
- Listing all divisors of 360 for a number theory problem
- Checking whether a number like 97 is prime
Frequently asked questions
- What is prime factorization?
- Prime factorization writes a number as a product of prime numbers, e.g. 60 = 2² × 3 × 5. Every integer greater than 1 has a unique prime factorization.
- How does the calculator find factors?
- It uses trial division: test divisibility by 2, then odd numbers 3, 5, 7, … up to √n, recording each prime factor as it divides the remaining value.
- Why are some divisor lists omitted?
- Highly composite numbers can have thousands of divisors. Lists are shown only when the count is 1,000 or fewer to keep the page responsive.
- What is the maximum input?
- Numbers up to 10,000,000,000 (10 billion) are supported.
