This is just a consequence of binary arithmetic isn't it ?
For starters, think base 10. If we have 100 and multiply by any other number the result will have at least two zeros at the end. If we multiply 1000 by any other number, the product wll have at least three zeros at the end, and so on.
The same sort of thing happens when numbers are written in binary, base two.
For example 4! (base 10) = 24 = 11000 (base 2).
Multiplying this by any number (base 2), the product will have at least three zeros at the end.
So, 5! = 5*4! = 120 (base 10) = 101 * 11000 = 1111000 (base 2).
That number at the end is