Prime Factorization Calculator
Break any number into its prime factors with exponents.
The Prime Factorization Calculator decomposes any number up to one trillion into its prime factors with exponents: 360 = 2³ × 3² × 5. It also reports the total divisor count and flags prime numbers when the decomposition is trivial.
Prime factorization is the backbone of number theory and shows up everywhere from cryptography to simplifying radicals and finding least common multiples. Every whole number greater than 1 has exactly one prime factorization — the fundamental theorem of arithmetic — which is why factorizations can identify and compare numbers.
The calculator uses exact trial division, which is fast and correct for the supported range. Results show exponents (2³ rather than 2×2×2) so large numbers stay readable. Runs locally in your browser.
Prime factorization
360 = 2^3 × 3^2 × 5
2
× 3
3
× 2
5
× 1
24
total divisors
Every whole number is a unique product of primes (the fundamental theorem of arithmetic). Trial division is exact for numbers up to 10¹².
How to use the Prime Factorization Calculator
- Enter a whole number from 2 to 1,000,000,000,000.
- Read the prime factorization with exponents.
- Check the divisor count.
- See the primality verdict if the number is prime.
- Verify: multiplying the factors returns your original number.
Frequently asked questions
What is a prime number?
A whole number greater than 1 with exactly two divisors: 1 and itself. 2, 3, 5, 7, 11 are prime; 1 is not prime by definition. Primes are the 'atoms' of multiplication.
Why are prime factors useful?
They are the common-denominator machinery: finding GCD and LCM, simplifying square roots, determining divisibility, and even generating secure encryption keys — large primes underlie RSA.
How large a number can this factor?
Up to 10¹² by exact trial division, which completes instantly for that range. Beyond roughly 10¹⁴, brute-force trial division becomes slow — real factorizers for cryptography-sized numbers use far more advanced algorithms.
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