Prime Factorization Calculator
Break any whole number into its prime factors, written with exponents, and check whether it is prime.
Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026
Result
360 = 2³×3²×5
Distinct prime factors: 2, 3, 5
360 is a composite number.
What is prime factorization?
Prime factorization breaks a whole number down into the prime numbers that multiply together to make it. A prime number is a whole number greater than 1 whose only divisors are 1 and itself (2, 3, 5, 7, 11, and so on). Every whole number greater than 1 has exactly one prime factorization, a result known as the fundamental theorem of arithmetic. Writing a number this way is the foundation for simplifying fractions, finding the greatest common factor and least common multiple, and working with roots and exponents.
How it's calculated
Start with the smallest prime, 2, and divide as many times as it goes in evenly. Move to the next prime (3, then 5, 7, and so on) and repeat, each time dividing out every copy of that prime. You only need to test primes up to the square root of the number; if nothing divides it by then, whatever remains is itself prime. The exponent on each prime simply counts how many times it appears.
Example
Take 360. It is even, so divide by 2 three times: 360, 180, 90, 45. Now 45 is divisible by 3 twice: 45, 15, 5. Finally 5 is prime. So 360 = 2 × 2 × 2 × 3 × 3 × 5, written with exponents as 2³ × 3² × 5.
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Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer
How to use
Enter any positive whole number from 2 up to 1,000,000,000,000. The calculator divides it by primes 2, 3, 5, 7, ... until nothing is left, then writes the result with exponents.
If the number is prime, the result is just the number itself. The list of distinct prime factors is shown below the factorization.