Prime Factorization Calculator
Find all prime factors of any positive integer. Decompose numbers into their fundamental prime components with detailed mathematical breakdown.
Prime Factorization Calculator
Find all prime factors of a positive integer. Maximum supported number: 9,007,199,254,740,991.
Enter a number above to find its prime factors
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About Prime Factorization
What is Prime Factorization?
Prime factorization is the process of breaking down a number into its prime factors - prime numbers that multiply together to give the original number. According to the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorization.
Examples:
Applications:
- Finding GCD and LCM
- Simplifying fractions
- Cryptography (RSA algorithm)
- Number theory research
Algorithm:
Our calculator uses trial division, testing divisibility by 2, then odd numbers from 3 up to ân. This ensures efficient factorization for numbers up to 9,007,199,254,740,991.