Break a number into its prime building blocks
Every whole number above 1 is either prime or a unique product of primes — the fundamental theorem of arithmetic. This calculator finds that product, shown in exponent form, and also reports the distinct primes, how many divisors the number has, their sum, and whether the number is prime.
How it factors
It uses trial division: pull out every factor of 2, then test odd numbers upward, dividing each out as many times as it goes. Once the test divisor squared passes what remains, anything left over is itself a prime factor. The exponents record how many times each prime appears.
What the extras tell you
From the exponents alone you get the divisor count — add one to each exponent and multiply — and the sum of divisors. These shortcuts mean you never have to list every divisor by hand to count or total them.
Related tools
To combine factorizations of several numbers, use the GCD and LCM calculator; to test a single number quickly, the prime number checker.
Worked example
360 factors as 2 to the 3rd times 3 squared times 5. Adding one to each exponent and multiplying (4 times 3 times 2) gives 24 divisors, which sum to 1170.
FAQ
Why is 1 not included?
One is neither prime nor composite and divides everything, so it is left out of prime factorizations by definition.
Are very large numbers slow?
Trial division is quick for everyday numbers but slows for huge values with large prime factors, since it must test divisors up to the square root.