Automatic dividing of a changing number

Hello,

I have a changing number in excel, at the moment this number is 1800, and right now this number can be divided by 600 so that the sollution is 3. But what if that number changes to say 2100, the sollution for the division '/600' will be different and will be a number with more digits after a comma, which is something I want to avoid. To get an even number the division would have to change to say 525, to get "4" as the sollution.
Is there a formula or another way to make excel determine by what number to divide to get a sollution that is between 3-6 and has no commas? Ideally this would happen automatically when the number in the cell changes.

I hope I made sense. Thanks in advance!

There might be more sophisticated algorithms out there, but, with only 4 possible solutions, I would probably set up a simple trial and error approach. First, some algebra:

The problem statement, if I understand it correctly, is Given a, we want to divide a by some number b that will give us an integer c between 3 and 6. So, c=a/b. Since b is the number we want to find, rearrange to solve for b b=a/c. Then set up the spreadsheet to compute the four possible divisors and determine which ones are integers. Those will be my possible solutions.

Example: 1800/3=600, 1800/4=450, 1800/5=360, 1800/6=300. Possible divisors are 600, 450, 360, 300. I'm not sure at this point how you will choose which one.
example: 2100/3=700, 2100/4=525, 2100/5=420, 2100/6=350. Possible divisors are 700, 525, 420, 350. I'm not sure how you will choose which one.