Prime Factorization Calculator
Decompose composite integers into their unique fundamental prime factor building blocks. By the Fundamental Theorem of Arithmetic, every integer greater than 1 possesses an invariant canonical prime factorization.
Enter an integer greater than 1
Prime factor powers notation (e.g. 2³ × 3² × 5)
How to Use This Calculator
- Enter the positive integer you wish to decompose.
- View the canonical prime factor power representation.
- Inspect the individual prime sequence, total prime count, and distinct divisors.
Formula & Calculation Methodology
The Fundamental Theorem of Arithmetic states that every integer n > 1 can be represented as a unique product of prime numbers raised to positive integer exponents.
Worked Example
Decomposing 360
Decomposing prime number 97
Frequently Asked Questions
What is the Fundamental Theorem of Arithmetic?↓
It states that every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers in a way that is unique up to order.
How does prime factorization help find GCD and LCM?↓
The GCD takes the lowest power of all common prime factors; the LCM takes the highest power of all prime factors appearing in either number.
Can 0 or negative numbers have a prime factorization?↓
Prime factorization is formally defined for positive integers ≥ 2. Negative numbers require factoring out -1.
What is a limitation of integer factorization algorithms?↓
Factoring enormous numbers (e.g. 2048-bit numbers used in RSA encryption) is notoriously difficult and forms the security foundation of modern internet cryptography.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.