C, trial division, 72 bytes

i=1;main(n){for(scanf("%d",&n);n%++i&&i*i<n;);printf("%d",n<3?n-1:n%i);} 

Note special handling for n=1,2

We need to stop the loop before i gets to n-1, so i<n-1 would do, but i*i<n is more efficient.