Prime Factorization Calculator
n = p₁^a₁ × p₂^a₂ × … Trial division to find all prime factors with multiplicity.
Result
Prime factorization
2^3 × 3^2 × 5
360 has 24 divisors.
- Number360
- Prime factors2, 3, 5
- Multiplicities2: 3, 3: 2, 5: 1
- Factored form2^3 × 3^2 × 5
- Number of divisors24
- Sum of divisors1170
Step-by-step
- 360 ÷ 2 = 180.
- 180 ÷ 2 = 90.
- 90 ÷ 2 = 45.
- 45 ÷ 3 = 15.
- 15 ÷ 3 = 5.
- 5 is prime — final factor.
How to use this calculator
- Enter positive integer.
- Read prime factorization + divisor count.
About this calculator
Every integer >1 has a unique prime factorization (Fundamental Theorem of Arithmetic). 360 = 2³ × 3² × 5. The number of divisors is the product of (exponent+1) terms: 360 has (3+1)(2+1)(1+1) = 24 divisors. Trial division is fastest for n < 10^12; beyond that, Pollard rho or quadratic sieve. Cryptographic security (RSA) relies on factoring being hard for products of two large primes.
Frequently asked
Fundamental Theorem of Arithmetic — every integer >1 has exactly one prime factorization (up to order). Proven by Euclid's lemma.
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