Prime Factorization Calculator
Break any number down into its prime factors
About this calculator
Prime factorization expresses a number as a product of prime numbers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). For example, 360 = 2³ × 3² × 5. This is foundational for finding GCF, LCM, simplifying fractions, and understanding number structure.
How to use
Enter 360. Divide repeatedly by the smallest prime: 360 ÷ 2 = 180 ÷ 2 = 90 ÷ 2 = 45 ÷ 3 = 15 ÷ 3 = 5. Result: 2³ × 3² × 5.
Frequently asked questions
Why is 1 not a prime number?
By definition, a prime has exactly two distinct factors: 1 and itself. The number 1 has only one factor (itself), so it does not qualify. Excluding 1 also preserves the uniqueness of prime factorization.
What is the largest prime number known?
As of 2024, the largest known prime has over 41 million digits. These are Mersenne primes of the form 2ⁿ − 1, found using distributed computing projects.