Prime Factorization Calculator
Break any whole number into its prime factors and see the factorization in exponent form. Also checks whether a number is prime and lists all its divisors.
Prime factorization of 360
2^3 Γ 3^2 Γ 5
= 2 Γ 2 Γ 2 Γ 3 Γ 3 Γ 5
Is it prime?
No β it's composite
Number of prime factors (with multiplicity)
6
All divisors (24)
Prime factorization breaks a number into the prime numbers that multiply together to make it. A prime number has exactly two divisors: 1 and itself. The calculator uses trial division up to the square root of the number.
Frequently Asked Questions
What is prime factorization?
Prime factorization expresses a number as a product of prime numbers. For example, 360 = 2Β³ Γ 3Β² Γ 5. Every whole number greater than 1 has exactly one prime factorization, a fact known as the Fundamental Theorem of Arithmetic.
How do I check if a number is prime?
A prime number has exactly two divisors: 1 and itself. To check, try dividing by every integer from 2 up to the square root of the number; if none divides evenly, it's prime. This calculator does that test for you and reports the answer.
Is 1 a prime number?
No. By definition a prime has exactly two distinct divisors, and 1 has only one divisor (itself). 2 is the smallest prime, and it is the only even prime number.
What does the exponent form mean?
When a prime factor repeats, it's written with an exponent. For example 8 = 2 Γ 2 Γ 2 is shown as 2Β³. The exponent tells you how many times that prime appears in the factorization, which makes large factorizations easier to read.
How is prime factorization used?
It's the basis for finding the GCD and LCM of numbers, simplifying fractions, and is central to cryptography β the security of RSA encryption relies on how hard it is to factor very large numbers into primes.