Prime Factorization Calculator
Find all prime factor steps for any positive integer. Fast, free, and fully client-side.
Calculator Inputs
Integer
Prime Factors—
How the Prime Factorization Calculator Works
Prime factorization breaks down a composite integer into the unique product of prime numbers that multiply together to equal the original value. By the Fundamental Theorem of Arithmetic, every integer greater than 1 has a single unique prime factorization.
Formula
N = p₁^a × p₂^b × ... × pₖ^n
Where p₁, p₂, etc. are prime factors and a, b are their respective integer powers.
Calculation Example
The prime factorization of 84 is 2 × 2 × 3 × 7, which can be written in exponential form as 2² × 3 × 7.
Frequently Asked Questions
What is a prime number?
A positive integer greater than 1 that has no positive divisors other than 1 and itself.
Why is 1 not considered a prime number?
Excluding 1 preserves the uniqueness property of the Fundamental Theorem of Arithmetic.