Math

Prime Factorization

Express any integer ≥ 2 as a product of primes to aid in simplification, divisibility checks, or number theory homework.

number theoryprimefactor
Prime Factorization

Decompose integers into their prime building blocks.

Prime factors
2 × 2 × 2 × 3 × 3 × 5
Factor count
6
Rebuilt value
360

Prime factorization identity

Every positive integer greater than 1 can be written uniquely as a product of prime numbers. The calculator repeatedly divides by the smallest available prime until only 1 remains.

How to use

  1. Enter an integer greater than or equal to 2.
  2. The tool strips out factors of 2, then continues testing odd numbers until the value is reduced to 1.
  3. Review the ordered list of prime factors, count, and rebuilt value for validation.

Example

Input: Number = 360

Output: Prime factors = 2 × 2 × 2 × 3 × 3 × 5

FAQ & notes

What if I enter a negative number?

The calculator uses the absolute value because prime factorizations are defined for positive integers. The sign can be reapplied afterward if needed.

Why does the factor list repeat primes?

Repeated primes show the multiplicity—or exponent—of each factor. For example, 360 includes 2 three times, so you can rewrite it as 2³ × 3² × 5.