G1.3 If 90 ! is divisible by $10^{k}$, where $k$ is a positive integer, find the greatest possible value of $k$.
Method 1
Method 2

When each factor of 5 is multiplied by 2 , a trailing zero We can find the total number of factors will appear in $n!$. of 5 by division as follow:

The number of factors of 2 is clearly more than the number
$590 \quad$ No. of factors of 5 is $18+3$ of factors of 5 in 280 !
It is sufficient to find the number of factors of 5 .
$5,10,15, \ldots, 90$; altogether 18 numbers, each have at least one factor of 5 .
$25,50,75$, altogether 3 numbers, each have at least two factors of 5 .
$\therefore$ Total number of factors of 5 is $18+3=21$
$$
k=21
$$