Prime Factorization Calculator
Find the prime factorization of any positive integer. See also GCF Calculator and LCM Calculator.
How to Find Prime Factorization
Prime factorization breaks a number down into a product of prime numbers. Start by dividing the number by the smallest prime (2), and continue dividing by primes until the result is 1. Each prime used is a factor, and the number of times it divides evenly is its exponent. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
Prime Factorization Method
1. Start with the smallest prime p = 2
2. While n is divisible by p, divide: n = n / p
3. Move to next prime and repeat
4. Continue until n = 1
n = p1^a1 × p2^a2 × ... × pk^ak
Total divisors = (a1+1)(a2+1)...(ak+1)
Example
Prime factorization of 360:
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 is prime
360 = 2³ × 3² × 5
Total divisors: (3+1)(2+1)(1+1) = 24
Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Is 1 a prime number?
No. By convention, 1 is not considered a prime number. This ensures the uniqueness of prime factorization (Fundamental Theorem of Arithmetic).
How is prime factorization used?
Prime factorization is used to find GCF and LCM, simplify fractions, solve problems in cryptography (RSA encryption), and analyze number properties.
Is prime factorization unique?
Yes. The Fundamental Theorem of Arithmetic states that every integer greater than 1 has a unique prime factorization, up to the order of the factors.