Prime Factorization Calculator

Find the prime factors of any integer and display the factorization tree.

Prime Factorization

360 = 2³ × 3² × 5

2

exponent: 3

2^3 = 8

3

exponent: 2

3^2 = 9

5

5^1 = 5

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How it works

Enter any positive integer. The tool divides it repeatedly by the smallest prime factors — starting at 2 — until the quotient is 1. It records each division step, collects the prime factors, and displays them with exponents in standard notation (e.g. 360 = 2³ × 3² × 5). A step-by-step breakdown shows every division. All computation runs locally in your browser.


              n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖ

Common use cases

  • Finding the GCD or LCM of two numbers by comparing their prime factors.
  • Simplifying fractions by factoring numerator and denominator.
  • Solving number theory homework problems requiring prime decomposition.

Frequently asked questions

What is the largest number I can factorize?

The tool uses trial division which works efficiently up to about 10^12. Very large numbers with large prime factors take longer but still complete in your browser.

Is 1 a prime number?

No. By definition, prime numbers must have exactly two divisors (1 and themselves). The number 1 has only one divisor, so it is neither prime nor composite.