Sumivo · Mathematics
Prime Factorization Calculator
Break a whole number into the product of its prime factors, with exponents — the unique prime factorization guaranteed by the fundamental theorem of arithmetic.
01 / inputs
02 / result
PRIME FACTORIZATION
2^3 × 3^2 × 5
- Factorization
- 2^3 × 3^2 × 5
- Distinct primes
- 3
- Prime?
- No
Calculation trace
- 2^3 = 88Factor out 2
- 3^2 = 99Factor out 3
- 55Remaining prime
How it works
Prime factorization writes a whole number as a product of prime numbers. The tool uses trial division: it divides by 2 as many times as possible, then by each odd number 3, 5, 7, … up to the square root of what remains, recording how many times each prime divides in. Any value left above 1 at the end is itself a prime factor. By the fundamental theorem of arithmetic, every integer greater than 1 has exactly one such factorization (apart from the order of the factors) — for example 360 = 2^3 × 3^2 × 5.
Assumptions & limits
- Defined for integers greater than 1; 1, zero, negatives, and decimals are rejected.
- Exponents show repeated primes, so 8 is written 2^3 rather than 2 × 2 × 2.
- Inputs are capped at 1,000,000,000,000 so the factorization stays fast in the browser.
FAQ
- What is prime factorization?
- It is writing a number as a product of prime numbers. For 12 the prime factorization is 2^2 × 3, meaning 2 × 2 × 3.
- Is the prime factorization of a number unique?
- Yes. The fundamental theorem of arithmetic says every integer greater than 1 has exactly one prime factorization, apart from the order in which you write the factors.
- What does it mean when a number has one prime factor?
- If the only prime factor is the number itself (with exponent 1), the number is prime — for example 17 = 17.
- Why can’t 1 be prime-factorized?
- 1 has no prime factors, and 1 is not itself prime, so it has no prime factorization. Prime factorization is defined for integers of 2 or more.
- How is prime factorization used?
- It is the basis for finding the greatest common factor and least common multiple, simplifying fractions, and much of number theory and cryptography.
Related calculators
SOURCES
- OpenStax, Rice UniversityPrealgebra 2e ↗
Prime factorization and the fundamental theorem of arithmetic
Accessed 2026-09-02