20! has 4 zeros because it has factors including 5,10,15 and 20. That gives us the factor 5 four times. There will always be enough 2s to pair up with the 5s.

25! has 6 zeros because you have factors 5, 10, 15, 20 and 25. That gives us the factor 5 six times.

Another example: 600! has 5,10,15....600 and 25,50,75...600 and 125,250,375,500. So how many zeros?

600/5=120

600/25=24

int(600/125)=4

I think that gives you 148 zeros.

The answer lies near here.