Basic Examples 
(9)
 

Find the number of factorials in the ceiling of  to the 100:
In[46]:=
[◼]
TrailingZeroes
[Ceiling[
100
E
]]
Out[46]=
6720292854540338621031563878950033968402747
This number is too large to compute the factorial for exactly:
In[47]:=
Ceiling[
100
E
]
Out[47]=
26881171418161354484126255515800135873611119
We effectively found the number of trailing zeroes in the number
⌈
100

⌉!=26881171418161354484126255515800135873611119!
.
When I was a student at the West Virginia 2018 State Math Field Day in 10th Grade at Marshall University there was a problem my team for Huntington High School had to solve together to find I think the number of zeroes in 2018! Find the answer:
In[55]:=
[◼]
TrailingZeroes
[2018]
Out[55]=
502
Calculate the number of trailing zeroes of 10! in base 12:
In[70]:=
[◼]
TrailingZeroes
[10,12]
Out[70]=
4
Find the number of trailing zeros of 100! in base 45:
In[71]:=
[◼]
TrailingZeroes
[100,45]
Out[71]=
24
Find the number of trailing zeros in the base-17 representation of
2017!
:
In[72]:=
[◼]
TrailingZeroes
[2017,17]
Out[72]=
124
Find the number of trailing zeros in the base-18 representation of
2018!
:
In[10]:=
[◼]
TrailingZeroes
[2018,18]
Out[10]=
502
Find the smallest integer N such that when N! is written in base 12, it has 121 trailing zeros. Enter your answer in base 6:
In[21]:=
BaseFormNestWhile#+1&,2,
[◼]
TrailingZeroes
[#,12]<121&,6
Out[21]//BaseForm=
1052
6
Let
a
3
be the highest power of 3 that divides 1000!. What is a? Source: Floor and Ceiling Functions: Level 2 Challenges Question 5
In[23]:=
[◼]
TrailingZeroes
[1000,3]
Out[23]=
498