Prime Factorization Calculator
Free prime factorization calculator: break any number up to one quadrillion into prime factors with exponents, and list all of its divisors.
What it does
Every whole number greater than 1 can be written as a product of prime numbers in exactly one way, apart from the order; this is the fundamental theorem of arithmetic. This calculator finds that product by trial division, shows it with exponents, tells you whether the number is prime and lists all of its divisors, whose count comes straight from the exponents.
How to use it
- Type a whole number from 2 to one quadrillion.
- See its prime factorization with exponents and whether it is prime.
- Check the number of divisors and the full list below.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
What is a prime number?
A whole number greater than 1 whose only divisors are 1 and itself, such as 2, 3, 5, 7, 11 and 13. The number 1 is not prime, and 2 is the only even prime.
How do I count the divisors from the factorization?
Add 1 to each exponent and multiply the results. 360 = 2³ × 3² × 5 has (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors.
How do I factor a number by hand?
Divide by the smallest prime that divides it exactly, 2, 3, 5, 7 and so on, and repeat with the result until you reach 1. You only need to test primes up to the square root of what is left.
Why is there a limit of one quadrillion?
Trial division is fast up to about 10^15 in a browser. Larger numbers can have prime factors so big that finding them needs much more advanced methods, which is what keeps internet encryption safe.
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