Amount of terminal zeroes in factorials in different bases

Question

I know this is a duplicate question or very close, but I haven't understood the answers I've come across so far. Can someone explain to me how to determine the amount of terminal zeroes that x! has in base y in layman's terms? Sorry if this is phrased badly or breaks any guidelines.

Answer 1

A zero is added

• every time a factor ends in $0$ (i.e. once every base),

• every time factors ending in divisors of the base combine with each other. If the base is highly composite there can be multiple combinations.

E.g. for base $10$,

$$10,20,30,40\cdots,2/5,12/15,22/25,\cdots$$