By "the integer" I presume you mean a number given by the user?
The first loop would probably be to make sure that the number is acceptable - some kind of input control. The second loop would be to cycle down the divisors, checking each to see if it is actually a divisor of the given number. So what exactly are you asking?
I think this is what you might be looking for Just 1 while loop was necessary, although it was a little difficult figuring out what you were trying to achieve. Good Luck