Prime factorization calculator
Break a number into its prime factors, and find out whether it is prime.
- Runs in your browser — nothing you enter is uploaded
- No sign-up, no quotas, free to use as often as you like
How it works
Every whole number above one is a product of primes in exactly one way. Finding that product is the basis of simplifying fractions, finding common denominators and most of elementary number theory.
How it factors
Trial division by 2, then by odd numbers up to the square root of what remains. Once the divisor exceeds that square root, whatever is left must itself be prime. That early stop is what makes the method fast enough to be instant for the numbers people actually type.
Exponent form
360 is 2 × 2 × 2 × 3 × 3 × 5, more usefully written 2³ × 3² × 5. The exponent form is what you need for finding highest common factors and lowest common multiples by hand.
Divisors
The number of divisors comes straight from the exponents: add one to each and multiply. 360 has exponents 3, 2 and 1, so it has 4 × 3 × 2 = 24 divisors. The sum of all divisors is given too, which is what identifies perfect and abundant numbers.
Limits
Up to a thousand million million. Beyond that, trial division becomes slow and floating-point whole numbers stop being exact — which is also, incidentally, why factoring large numbers underpins public-key cryptography.
Prime factorization calculator — questions
How do I know if a number is prime?
If it has exactly one prime factor — itself. The tool states it directly.
What is exponent form?
Repeated factors collected together: 2 × 2 × 2 × 3 × 3 × 5 becomes 2³ × 3² × 5.
How is the divisor count worked out?
Add one to each exponent and multiply them together.
How large a number can it handle?
Up to 10¹⁵. Beyond that the method is too slow and whole numbers stop being exactly representable.
Is 1 prime?
No. Primes have exactly two distinct divisors, and 1 has one. The tool requires a number of 2 or more.