Finding all the zeroes in $100!$

Question

Is there a way to find all the $0$s in $100!$? (Including zeroes that come between two non-zero numbers)

I know that to find the $0$s at the end we can use the greatest integer method. I was just curious if a method exists to find the remaining zeroes, too. (Of course without finding the actual value of $100!$ and counting, as is done in the only answer to this previous question: How many zeroes are in 100!.)

Answer 1

One way is to compute it!

In[2]:= Count[IntegerDigits[100!], 0]
Out[2]= 30

This computation took 0.000033 seconds in Mathematica.