Prime Factorization Calculator
Find the prime factors of a number.
Runs locally in your browser
Your inputs are processed locally in your browser and are not uploaded or stored by us.
The Prime Factorization Calculator expresses a positive integer as a product of prime powers.
How to find prime factors
- Enter a positive integer in the input field.
- Click "Calculate" to generate the prime factorization.
- The result displays the unique prime factors along with their respective exponents.
Factorization Algorithm
n = p₁^e₁ × p₂^e₂ × ... × pₖ^eₖ
The algorithm removes the factor 2 repeatedly, then tests odd divisors sequentially, stopping when the squared divisor exceeds the remaining value.
Prime factorization of 60
Number60
60 = 2 × 2 × 3 × 5
Result: 2² × 3 × 5
Notes
- The calculator accepts positive safe integers greater than or equal to 1. (e.g., 12 = 2² × 3, 97 = 97, 1024 = 2¹⁰).
- Negative inputs and zero are not supported in this version.
- The special case of 1 has no prime factors and is not prime.
- The current browser-based implementation intentionally limits inputs to 1,000,000,000,000 so factor searches remain bounded and responsive. This is a deliberate browser-performance guardrail, not a mathematical limit on prime factorization itself.
- The calculator preserves exact integer relationships within its documented limits.
- Your inputs are processed locally in your browser and are not uploaded or stored by us.