🔍 Prime Factorization Calculator
Find prime factors of any number
Enter a positive integer (2 or greater)
How Prime Factorization Works
- 1Enter a positive integer.
- 2The calculator tests divisibility starting from the smallest prime (2).
- 3Each time a prime divides the number evenly, it's recorded as a factor.
- 4The process continues with the quotient until it reaches 1.
- 5The result shows all prime factors with their exponents (e.g., 360 = 2³ × 3² × 5).
About Prime Factorization Calculator
Find the prime factorization of any number. Break down integers into their prime factors with step-by-step division. Check if a number is prime. Includes factor tree visualization.
Frequently Asked Questions
What is prime factorization?
Prime factorization is breaking a number into a product of prime numbers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). For example, 60 = 2² × 3 × 5.
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The number 2 is the only even prime.
How large a number can this factor?
The calculator handles numbers into the billions efficiently using trial division. Extremely large numbers (hundreds of digits) require advanced algorithms. For everyday use, it handles any practical number instantly.