How it works
Every whole number greater than 1 is either prime (its only divisors are 1 and itself) or can be written as a product of primes in exactly one way. 360 = 2³ × 3² × 5.
The calculator uses trial division up to the square root of the number, which is enough to find every factor. From the factorization it also counts the divisors: multiply one more than each exponent, so 360 has (3+1)(2+1)(1+1) = 24 divisors.
Formula
n = p₁^a₁ × p₂^a₂ × …; number of divisors = (a₁ + 1)(a₂ + 1)…
Questions people ask
Is 1 a prime number?
No. A prime has exactly two distinct divisors, and 1 has only one. Excluding 1 is what makes prime factorizations unique.
How do I check if a number is prime by hand?
Try dividing by every prime up to its square root. To test 97, try 2, 3, 5 and 7 (since √97 ≈ 9.8); none divides it, so 97 is prime.
What is prime factorization used for?
Finding the GCF and LCM, simplifying fractions and radicals, and in cryptography, where multiplying large primes is easy but factoring the product is extremely hard.