What is the Maximum Number of Divisions problem and how can it be solved using a greedy algorithm?

What is the Maximum Number of Divisions problem and how can it be solved using a greedy algorithm?

The Maximum Number of Divisions problem is a problem where we are given a positive integer N and we need to find the maximum number of divisions we can perform on N such that the result of each division is still a positive integer.

To solve this problem using a greedy algorithm, we can follow these steps:

1. Initialize a variable count to 0, which will keep track of the number of divisions performed.
2. Start with N as the current number.
3. While the current number is divisible by 2, divide it by 2 and increment the count by 1.
4. While the current number is divisible by 3, divide it by 3 and increment the count by 1.
5. Repeat steps 3 and 4 until the current number is no longer divisible by 2 or 3.
6. The final value of count will be the maximum number of divisions that can be performed on N.

This greedy algorithm works by continuously dividing the current number by 2 and 3, as these are the smallest prime numbers. By doing so, we ensure that we are dividing the number as much as possible, maximizing the number of divisions.