Prime Factorization Calculator
Enter any integer 2 or greater to see its prime factorization. The calculator returns both the expanded list of prime factors and the compact prime power form.
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Understanding prime factorization
A prime number has exactly two positive divisors: 1 and itself. Prime factorization expresses a whole number as a product of primes.
Every integer greater than 1 has a unique prime factorization. This is known as the Fundamental Theorem of Arithmetic.
The expanded form lists every prime factor, while the prime power form groups equal primes using exponents, such as 360 = 2^3 x 3^2 x 5.
This calculator uses trial division by small primes up to the square root of the input, which is an efficient and reliable way to find factors.