Find largest dividing integer within range Is there a neat way to find the largest integer that divides another integer fully, within a range. As an example, I would like to find the largest integer smaller than 1131 that divides 3500 completely. 
So far I have just tried by breaking up 3500 into its prime components and guessing, coming to 875, but is there a more structured way?
EDIT: I guess the problem is somewhat equivalent to get all dividing integers, and then just pick the largest within my range?

You could look for the smallest integer greater than $\dfrac{3500}{1131}\approx 3.09$ that divides $3500$ exactly  
This is obviously $4$ (there is no smaller integer greater then $3.09$ and $4$ does divide $3500$ as it divides $100$) so the answer to your original question is $\dfrac{3500}{4}=875$
