The prime factorization calculator finds the prime factors of any integer and displays them in factor form (2³ × 3 × 5) with a step-by-step factor tree showing each division.
Prime Factorization Calculator
How to Use the Prime Factorization Calculator
Prime factorization expresses any integer as a product of prime numbers. The Fundamental Theorem of Arithmetic guarantees this factorization is unique for every positive integer greater than 1.
How the Algorithm Works
The calculator uses trial division: divide by 2 repeatedly, then try 3, 5, 7, 11, etc. up to √n. Each successful division reveals a prime factor. Example: 360 ÷ 2 = 180, ÷2 = 90, ÷2 = 45, ÷3 = 15, ÷3 = 5 (prime). Result: 2³ × 3² × 5.
Applications
Prime factorization is used to find GCF and LCM (by comparing factor lists), simplify fractions, and understand number theory. In cryptography, factoring large numbers (hundreds of digits) is computationally infeasible — the basis of RSA encryption.
Number of Divisors
If n = p₁^a₁ × p₂^a₂ × ..., then the total number of divisors = (a₁+1)(a₂+1).... For 360 = 2³×3²×5¹: divisors = (3+1)(2+1)(1+1) = 4×3×2 = 24. So 360 has exactly 24 divisors.
FAQ
What is prime factorization?
Prime factorization expresses a number as a product of prime numbers. Every positive integer > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). Example: 360 = 2³ × 3² × 5. The prime factors of 360 are 2, 3, and 5.
How do you find the prime factorization of a number?
Use trial division: divide by 2 repeatedly until odd, then try 3, 5, 7, 11, etc. up to √n. Each successful division gives a prime factor. Example: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5. So 60 = 2² × 3 × 5.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
What is the largest number I can factor?
The calculator handles integers up to 10 billion. For larger numbers, factorization becomes computationally intensive. Note that very large primes are computationally difficult to factor — this is the basis of RSA cryptography.