Prime Factorization Calculator
Enter a whole number to break it into prime factors, shown with exponents.
Break any number into primes
Every whole number above 1 is a unique product of prime numbers — the building blocks of arithmetic. This calculator finds that factorization, which underpins reducing fractions, finding divisors, and understanding a number’s structure.
It shows both forms: 360 expands to 2 × 2 × 2 × 3 × 3 × 5 and condenses to 2³ × 3² × 5. Reading the exponents tells you at a glance how many divisors the number has and which primes dominate it.
Efficient and private
It uses trial division up to the square root, so the remainder is guaranteed prime and the work stays quick for everyday numbers. The factoring runs entirely in your browser.
Frequently Asked Questions
How does it factor the number?
By trial division: it divides out 2s, then odd numbers up to the square root of what remains, so the leftover is always prime. This is fast for typical inputs.
How large a number can it handle?
Comfortably into the billions. Very large semiprimes (two huge primes multiplied) are hard for any simple method and may be slow.
What is the output format?
Both the expanded product and the exponent form, e.g. 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
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