Number theory

Prime Factorization Calculator

Break a whole number into prime factors and exponent notation.

Prime factors are building blocks

Prime factorization supports GCF, LCM, simplifying radicals and checking divisibility. This page is intended for educational-sized integers, not cryptographic-scale factoring.

Example

360 breaks into 2 x 2 x 2 x 3 x 3 x 5, which can also be written as 2^3 x 3^2 x 5. Multiplying those factors returns the original number.

Common mistakes

Prime factorization uses prime numbers only. For example, 12 is a factor of 360, but it is not a prime factor because 12 can still be split into 2 x 2 x 3.

Limitations

The calculator is designed for normal classroom and practical integer work. Very large numbers can be slow to factor and may need specialized number theory software.

Last reviewed: 2026-05-17

Before relying on this result

Use this calculator together with the formula, assumptions, limitations and examples on the page. If the topic involves health, tax, lending, investment, legal, safety or current-rate decisions, treat the number as an estimate and check the relevant primary source or professional guidance.

Calculator metadata last reviewed: 2026-05-14.