Prime Factorization Calculator

Prime factorization and primality

Every whole number greater than 1 is either prime or can be written as a unique product of primes. This tool tells you whether your number is prime and, if not, breaks it into its prime factors with their exponents — for example 360 = 2³ × 3² × 5.

What you get

• Factored form — the primes and their powers.
• Prime factors — the full list with repeats.
• Number of divisors — found by adding one to each exponent and multiplying.

FAQ

How does it stay fast for big numbers?

It only tests divisors up to the square root of the number — once you pass that point, any remaining value is itself prime. That keeps even large inputs near-instant.

Is this prime factorization tool free and private?

Yes — it's free with no sign-up, and the factorization runs entirely in your browser. The number you enter is never sent to a server, so you can use it freely for homework, cryptography study, or anything else.

Is 1 a prime number?

No. By definition a prime has exactly two distinct divisors, 1 and itself, so the number 1 doesn't qualify. It has no prime factorization, and 2 is the smallest prime.

How does it count the number of divisors?

It uses the factored form: add one to each prime's exponent and multiply those together. For example 360 = 2³ × 3² × 5 gives (3+1)(2+1)(1+1) = 24 divisors, without having to list them all.

What's the largest number it can factor?

Because it only tests divisors up to the square root, even fairly large numbers factor quickly. Very large numbers with two huge prime factors (the kind used in cryptography) are deliberately hard for any tool and may take longer, which is exactly why such numbers are used for security.

Does it work on mobile?

Yes. It's responsive and runs in any mobile browser, so you can check primality or factor a number on a phone just as fast as on desktop.