i'm pretty sure you make all the bases 100 and then it would be easier to tell
The number of zeros a number has is the same as the number of 10s it has.
For example 200 has 2 tens. 2 * 10^2, so it has 2 zeros. 120 has 1 ten, 12 * 10, so it has 1 zero.
The number of tens a number has is equal to the number of two and five pairs it has since 2*5 = 10.
In the number above, there are 12 twos and 15 fives, meaning you can have 12 pairs of 2 and 5.
So there are 12 zeros.