math
Prime Factorization Calculator
Break a whole number down into its prime factors, with exponents.
Prime factorization
2^3 × 3^2 × 5
Written as a product of primes, with exponents.
How it works
- 1Enter a whole number of 2 or more.
- 2The number is divided by primes from smallest to largest.
- 3The result is the product of primes, with exponents (e.g. 360 = 2^3 × 3^2 × 5).
Use cases
- Find the prime factors of a number.
- Build a factor tree for homework.
- Use the factorization to find GCD or LCM.
Frequently asked questions
What is prime factorization?
Expressing a number as a product of prime numbers. For example, 360 = 2 × 2 × 2 × 3 × 3 × 5, written 2^3 × 3^2 × 5.
Is the factorization unique?
Yes. By the fundamental theorem of arithmetic, every whole number above 1 has exactly one prime factorization.
What about prime inputs?
A prime number factorizes to itself — for example, 7 = 7.
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