remainder, when 16! is divided by 17?

The answer is 16 and it can be easily solved using the Wilson's theorem.

Why don't you go through all the remainder theorems and Number Systems formulas for CAT here.

If p is a prime, then (p-1)!+1 is a multiple of p (Wilson's theorem). ( 17 -1)! +1 will be divisible by 17 .Hence the remainder is 16