Prime factorization
Factor any integer, list its divisors and test primality.
2 × 2 × 2 × 3 × 3 × 5
Product of (exponent + 1)
Comparing the sum of proper divisors to the number itself
Factor tree
All 24 divisors
How it works
Every integer greater than 1 is either prime or a product of primes, and that product is unique apart from the order of the factors. This is the fundamental theorem of arithmetic, and it is why primes are called the building blocks of the integers.
360 = 2³ × 3² × 5 How the divisor count works
Once you have the prime factorisation, you get the number of divisors for free. Each divisor picks an exponent for every prime, from zero up to its full power — so 2³ × 3² × 5¹ has (3+1)(2+1)(1+1) = 24 divisors, without listing a single one.
Perfect, abundant and deficient
Add up a number's proper divisors (everything below itself). If they sum to exactly the number, it is perfect — 6 = 1+2+3, and 28 = 1+2+4+7+14. More than the number is abundant, less is deficient. Only 51 perfect numbers are known, and nobody has ever found an odd one.
Why this is slow for big numbers
This tool divides by candidate factors up to √n, which is fast for anything you can type but hopeless for the hundreds-of-digits numbers used in cryptography. RSA rests entirely on that asymmetry: multiplying two large primes is instant, and undoing it is not.