Prime Factorization Calculator

Find the prime factorization of any positive integer.

Result

Fill in the fields above, then press Calculate.

A prime factorization calculator decomposes any positive integer into its unique product of prime factors.

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.

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.
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Factor Calculator
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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.