Question

How many zeros are there in $100!$ ?

Answer 1

Compute the required number:

Dividing $100$ by $5$ and its subsequent quotients by $5$as long as the quotient is nonzero or divisible by $5$ (ignore remainder).

$\frac{100}{5}\stackrel{}{\to }quotient=20$

$\frac{20}{5}\stackrel{}{\to }quotient=4$

Adding all non-zero quotients.

Total number of zeroes in $100!$$=20+4$

Total number of zeroes in $100!$$=24$

Hence, there are $24$ zeroes in $100!$ .