Math
Prime Factorization Calculator
Factor any integer up to 10¹² into its prime components with exponents.
Inputs
Prime Factorization Calculator
Result
Prime factorization of 360
2³ × 3² × 5
- Distinct primes
- 2 (×3), 3 (×2), 5 (×1)
- Is prime?
- No
How it's calculated
Every integer n > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
Common questions
Why the 10¹² limit?
Trial division stays fast (√n ≈ 10⁶ iterations). Larger numbers need specialised algorithms.
Is 1 prime?
No — by convention 1 is neither prime nor composite.
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