Prime Factorization Calculator

Prime Factorization – Quick Cheat Sheet

• Prime factorization: express n as product of primes: n = p1e1 × p2e2 × …
• Expanded multiplication: repeats each prime e_i times (e.g., 360 = 2×2×2×3×3×5).
• ω(n) (omega, lowercase): number of distinct primes.
• Ω(n) (Omega, uppercase): total prime factors counting multiplicity.
• τ(n) (divisor count): ∏ (ei + 1).
• σ(n) (divisor sum): ∏ ( (piei+1 − 1) / (pi − 1) ).
• φ(n) (Euler’s totient): n × ∏ (1 − 1/pi).
• Performance tip: this tool factors quickly up to about 1,000,000,000,000 using trial division with a 6k±1 wheel.