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Enter a whole number (2 or greater) to see its prime factorization.
A prime number is a whole number greater than 1 whose only divisors are 1 and itself: 2, 3, 5, 7, 11, 13 and so on. Every whole number greater than 1 can be written as a product of primes in exactly one way, apart from the order. This is the fundamental theorem of arithmetic, and that product is the number's prime factorization.
Prime factors show the structure of a number. They make it easy to simplify fractions, find GCDs and LCMs, simplify square roots, and count how many divisors a number has.
It uses trial division: divide by 2 as many times as possible, then by 3, then 5, and so on through larger candidates. You only need to test divisors up to the square root of what's left. If nothing divides it by then, the remaining number is itself prime.
So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32 × 5. To count its divisors, add 1 to each exponent and multiply: (3+1) × (2+1) × (1+1) = 24 divisors.
No. A prime must have exactly two distinct divisors, and 1 has only one. Excluding 1 is also what makes every number's prime factorization unique.
Yes. Every other even number is divisible by 2, so it has at least three divisors (1, 2 and itself).
Pair up identical primes. For √360 = √(2² × 2 × 3² × 5), each pair comes out as a single factor: 2 × 3 = 6, leaving √(2 × 5). So √360 = 6√10.
Multiplying two large primes is easy, but factoring the result back is extremely slow. That one-way difficulty is the basis of RSA encryption, which helps secure much of the internet.