# How to find the number of trailing zeros in a factorial?

E.g you have to find the number of trailing zeros of 28! in base 5.

How would you go about it without writing 28! in base 5? Is there a certain step by step method?

I already wrote 28! as a product of its primes.

28! = 2^25 * 3^13 * 5^6 * 7^4 * 11^2 * 13^2 * 17 * 19 * 23

The number of trailing zeros of an integer $$n$$ expressed in base-$$b$$ is equal to the greatest value of $$k$$ such that $$b^k \mid n$$, so in this case you need to find the greatest power of $$5$$ that divides $$28!$$.