Prime Factorization Tool

Prime factorization is the process of expressing a positive integer as a product of its prime factors — numbers greater than 1 that have no divisors other than 1 and themselves. Every integer greater than 1 has a unique prime factorization, a fact known as the Fundamental Theorem of Arithmetic. For example, 360 = 2³ × 3² × 5, meaning 360 is the product of three 2s, two 3s, and one 5. Our prime factorization tool uses the trial division algorithm to systematically divide the input by each prime starting from 2, recording each factor until the quotient reaches 1. The result is expressed in exponential notation for clarity.

1. 1. Enter Your Number: Type any positive integer from 2 to 1,000,000,000,000 (one trillion). All processing happens locally in your browser — your data never leaves your device.
2. 2. Instant Factorization: Click Factorize and the tool applies trial division, testing each prime divisor starting from 2. Each successful division is recorded as a step. If the number is prime, it is identified immediately.
3. 3. Review Full Results: View the prime factorization in exponential notation, a step-by-step division table, all positive divisors, and number properties including divisor count, divisor sum, and whether the number is perfect.

• Prime Factorization: The unique product of prime powers that equals the input number, written in exponential notation (e.g. 2^3 × 3^2 × 5 for 360).
• All Divisors: Every positive integer that divides the number evenly, derived from the prime factorization. A number n = p₁^a × p₂^b has (a+1)(b+1) divisors total.
• Number of Divisors (τ): The total count of positive divisors, computed as the product of (exponent + 1) for each prime factor.
• Sum of Divisors (σ): The sum of all positive divisors. If the sum of proper divisors (all divisors except the number itself) equals the number, it is a perfect number (e.g. 6 = 1 + 2 + 3, 28 = 1 + 2 + 4 + 7 + 14).

A prime number is a positive integer greater than 1 with exactly two divisors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23... The Fundamental Theorem of Arithmeticstates that every integer greater than 1 is either prime or can be expressed as a unique product of primes (up to the order of factors). This uniqueness is what makes prime factorization so powerful — it is the "fingerprint" of every number. Our prime factorization tool identifies prime inputs immediately and displays a special indicator, so you always know whether your number is prime or composite.