Prime Factorization Calculator
Enter a whole number to find its complete prime factorization — the unique set of prime numbers that multiply together to produce it.
Prime factorization
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Enter a number to factor.
How the Prime Factorization formula works
Every whole number greater than 1 has a unique prime factorization (the Fundamental Theorem of Arithmetic):
Repeatedly divide by the smallest prime that evenly divides the number, until only 1 remains
Step-by-step calculation
- Start with the smallest prime, 2, and divide it out of the number as many times as it evenly divides.
- Move to the next prime (3, then 5, then 7...) and repeat.
- Continue until the remaining number is reduced to 1 — the primes used, with their counts, are the factorization.
Worked example
84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7. So 84 = 2² × 3 × 7.
Frequently asked questions
Why is prime factorization useful?
It's a foundational tool for finding greatest common divisors, least common multiples, simplifying fractions and radicals, and it underlies much of number theory and cryptography.
What's the factorization of a prime number itself?
A prime number's factorization is just itself — for example, 17 is already prime, so its factorization is simply 17¹, with no other factors to break it down further.