Prime Factorization Calculator
Express an integer as a product of prime powers, and check whether it is prime.
Runs 100% in your browser — nothing is uploaded.
Result
Formula
Every integer > 1 is a unique product of primes (fundamental theorem of arithmetic).
About this calculator
The Prime Factorization Calculator expresses any integer greater than 1 as a unique product of prime powers, following the fundamental theorem of arithmetic. It also indicates whether the input number is prime. The calculator performs trial division by prime numbers up to the square root of the input.
How to use
- 1
Enter a whole number between 2 and 100,000,000 in the 'Number' field.
- 2
Click the calculate button to see the prime factorization.
- 3
Review the results: the prime factorization, the expanded form, and whether the number is prime.
Frequently asked questions
What is prime factorization?
Prime factorization is the process of expressing a number as a product of its prime factors. For example, 12 = 2 × 2 × 3 = 2^2 × 3.
Why is 1 not included in prime factorization?
1 is not a prime number and has no prime factors. The fundamental theorem of arithmetic applies to integers greater than 1.
How do you determine if a number is prime?
A number is prime if it has exactly two distinct positive divisors: 1 and itself. The calculator checks divisibility by primes up to the square root of the number.
Please note: Results are estimates for general information only and are not professional or medical/financial advice.