Prime Factorization Calculator

Prime factorization writes a whole number as a product of prime numbers. For example 360 = 2 x 2 x 2 x 3 x 3 x 5, which is shortened to 2^3 x 3^2 x 5. Every integer above 1 has exactly one such factorization.

It uses trial division: it repeatedly divides the number by 2, then by each odd number, up to the square root of what remains. Any leftover value above 1 is itself a prime factor. This finds the complete factorization for everyday numbers.

When a prime appears more than once, it is written as a power. So 2^3 means 2 used three times (2 x 2 x 2) and 3^2 means 3 used twice. A prime that appears only once is written on its own, like the 5 in 2^3 x 3^2 x 5.

A prime number has no factors other than 1 and itself, so its factorization is just the number. The calculator flags it as prime and shows a single entry in the factor table.

Prime factorization is defined for whole numbers that are 2 or greater. The numbers 0 and 1 have no prime factorization, and decimals and negatives fall outside the definition, so the tool asks for a counting number instead.

Yes. The factorization runs entirely in your browser. Nothing you type is sent to a server, so your numbers stay on your device.