Prime Factorization Calculator
Break any positive integer into its prime factors. See the factors, their counts, and the exponential notation.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter any positive integer (2 or greater) to see its complete prime factorization. The result shows the prime factors in exponential notation with a table of each factor and its count.
- Enter a number. Type any integer of 2 or greater.
- Read the result. The prime factorization appears in exponential form (like 2^3 x 3^2 x 5). A table below shows each prime factor and how many times it appears.
- Prime detection. If the number itself is prime, the calculator tells you so.
The algorithm divides by 2, then by odd numbers starting from 3, collecting factors until the remaining value is 1. This trial division method works efficiently for numbers up to several billion.
About Prime Factorization
Every positive integer greater than 1 can be expressed as a unique product of prime numbers. This is the Fundamental Theorem of Arithmetic. Prime factorization is the process of finding that product. It is the basis for understanding divisibility, computing GCDs and LCMs, and is central to cryptography (RSA encryption relies on the difficulty of factoring large numbers).
A prime number has no factors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Every composite number can be broken down into a product of these building blocks.
Frequently Asked Questions
What is prime factorization?
Prime factorization is expressing a number as a product of prime numbers. For example, 360 = 2^3 x 3^2 x 5. Every integer greater than 1 has a unique prime factorization.
How do you find prime factors?
Start dividing by the smallest prime (2). Keep dividing by 2 until it no longer divides evenly. Move to 3, then 5, and so on. Each time a prime divides the number, record it as a factor. Continue until the remaining number is 1.
Is 1 a prime number?
No. By modern convention, 1 is not a prime number. Primes must have exactly two distinct positive divisors: 1 and themselves. The number 1 has only one divisor (itself), so it does not qualify. Excluding 1 preserves the uniqueness of prime factorization.