Prime Factorization Calculator
Find the prime factorization of any positive integer.
A prime factorization calculator decomposes any positive integer into its unique product of prime factors.
Examples
360
84
Prime number
Frequently Asked Questions
What is a prime number?
What is the Fundamental Theorem of Arithmetic?
How is the number of divisors calculated?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use prime factorization to find the GCD or LCM of two numbers.
- •Check if a number is prime — its only factorization will be itself.
A prime factorization calculator decomposes any positive integer into its unique product of prime factors.
How to Use This Calculator
Enter a positive integer greater than 1. The calculator will decompose it into its prime factors, show the factor tree steps, and display additional information like the number of divisors.
Understanding the Formula
Every integer > 1 can be uniquely represented as a product of prime numbers (Fundamental Theorem of Arithmetic): n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ
Examples
360
360 = 2³ × 3² × 5 = 2 × 2 × 2 × 3 × 3 × 5
84
84 = 2² × 3 × 7 = 2 × 2 × 3 × 7
Prime number
97 = 97 (97 is prime, its only factorization is itself)
Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
What is the Fundamental Theorem of Arithmetic?
Every integer greater than 1 either is prime or can be uniquely expressed as a product of prime numbers (up to the order of factors).
How is the number of divisors calculated?
If n = p₁^a₁ × p₂^a₂ × ... then the number of divisors = (a₁+1)(a₂+1)... For 360 = 2³×3²×5¹: (3+1)(2+1)(1+1) = 24 divisors.
Assumptions & Limitations
- Assumes integer input greater than 1.
- Assumes exact input values; rounding in inputs propagates to results.
- Performance may degrade for very large numbers approaching the upper input limit.