MATH · PRIME FACTORIZATION
Prime Factorization Calculator
Find the prime factorization of any number up to 10¹⁵. See the prime factors and exponent notation instantly.
Prime Factorization
2² × 3 × 5
60 = 2² × 3 × 5
Factor2 (×2)
Factor3
Factor5
All factors2 × 2 × 3 × 5
About This Calculator
Enter any whole number ≥ 2 and this calculator instantly decomposes it into its prime factors with exponent notation. Works for numbers up to 10¹⁵ and correctly identifies prime numbers.
How It Works
The calculator uses trial division, testing each integer from 2 up to √n. When a divisor is found it is recorded and n is divided repeatedly until it no longer divides evenly, then the process continues with the next candidate. Any remainder > 1 after the loop is itself a prime factor.
The Formula
n = p₁^e₁ × p₂^e₂ × … × pₖ^eₖ
- n
- the number to factorize
- pᵢ
- distinct prime factors
- eᵢ
- exponent (how many times pᵢ divides n)
Frequently Asked Questions
- What is prime factorization?
- Prime factorization (also called prime decomposition) is expressing a whole number as a product of its prime factors. For example, 60 = 2² × 3 × 5. Every integer greater than 1 has exactly one prime factorization (Fundamental Theorem of Arithmetic).
- How do I read the exponent notation?
- The notation 2³ × 5 means the prime 2 appears three times (2 × 2 × 2 = 8) and the prime 5 appears once. Multiplied together, 8 × 5 = 40.
- What is the largest number this calculator can handle?
- The calculator supports numbers up to 10¹⁵ (one quadrillion). Above that, trial division becomes very slow in a browser and the result field is capped to keep the page responsive.
- How do I check if a number is prime?
- Enter the number. If the result shows it is prime, no factorization exists — the number is only divisible by 1 and itself. If it returns a factorization, it is composite.