discrete mathematics - Determine the number of 0 digits at the end of 100!

I got this question, and I'm totally lost as to how I solve it! Any help is appreciated :)

When 100! is written out in full, it equals 100! = 9332621...000000. Without using a calculator, determine the number of 0 digits at the end of this number

EDIT: Just want to confirm this is okay --

I got 24 by splitting products into 2 cases 1) multiples of 10 and 2) multiples of 5 Case I (1*3*4*6*7*8*9*10)(100,000,000,000)--> 12 zeroes

Similarly got 12 zeroes for Case 2.

So 24 in total? Is that correct?