Prime Factorization Calculator

Decompose any number into its prime factors instantly

Calculator

Numbers between 2 and 999,999,999,999,999

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What is Prime Factorization?

Prime factorization is the process of breaking down a composite number into the product of its prime factors. Every composite number can be expressed as a unique product of prime numbers (this is known as the Fundamental Theorem of Arithmetic).

Example:

The number 72 can be factorized into primes as:

72 = 2 × 2 × 2 × 3 × 3

Or using exponents: 72 = 23 × 32

How to Use This Calculator

  1. Enter any positive integer greater than 1 (up to 15 digits)
  2. Click "Calculate Prime Factors"
  3. View the prime factors in expanded and exponential form
  4. Click "Show Factor Tree" to see the step-by-step factorization

Fast Calculation

Instantly factorizes numbers up to 15 digits using optimized algorithms.

Factor Tree

Visualize the factorization process with a detailed factor tree diagram.

Calculation History

Keep track of your recent calculations for reference.

Applications of Prime Factorization

Mathematics

Essential for finding greatest common divisors (GCD), least common multiples (LCM), and simplifying fractions.

Cryptography

Forms the basis of RSA encryption and other public-key cryptographic systems.

Computer Science

Used in algorithm design, particularly in number-theoretic algorithms.

Education

Fundamental concept in elementary number theory and school mathematics.