Since we need to divide so the quotient should be at least 1, and we need 
greatest remainder, so we need the least no. which will give the quotient 1 
upon dividing and that would be the no. you described.
Also you would have noted the greatest remainder would be  floor(n/2)-1 .

On Thursday, 16 May 2013 13:56:40 UTC+5:30, Soumya Prasad Ukil wrote:
>
>
> For a given number when divided by a number between 1 and n. I figured out 
> that highest reminder can be got if I divide the number by (⌊(n/2)⌋+1).Can 
> anyone give me pointers ?
>

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