Prime FactorizationFind the prime factors of any number with expanded form and divisor count.

The algorithm uses trial division: starting with the smallest prime (2), repeatedly divide the number as long as it's divisible, counting the exponent. Then move to the next potential factor (3, 4, 5, ...). We only need to test up to √n because if n has a factor greater than √n, the corresponding cofactor must be less than √n and would have been found already. After the loop, if the remaining number is greater than 1, it is itself a prime factor. Time complexity is O(√n) in the worst case (when n is prime). The divisor count formula derives from the multiplicative nature of the divisor function: each prime power p^a contributes (a+1) choices (p^0, p^1, ..., p^a) when building divisors, and these choices are independent across different primes, so the total count is the product of (aᵢ+1) for all prime factors. For example, 360 = 2³ × 3² × 5¹ has (3+1)(2+1)(1+1) = 24 divisors.