The largest non-negative integer $k$ such that $24^k$ divides $13!$ is

Three players play a total of $9$ games. In each game,one person wins and the other two lose; the winner gets $2$ points and the losers get $-1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is

If $a$ is the number of all even divisors and $b$ is the number of all odd divisors of the number $10800$,then $2a+3b=$

If $n=(210)^2(360)(143)$,then the total number of non-trivial factors of $n$ is

Among the positive divisors of the number $12600$,if $n_1$ is the number of divisors which are multiples of $3$ and $n_2$ is the number of divisors which are multiples of $14$,then $n_1 + n_2 =$

What is the number of divisors of $n = 38808$ (excluding $1$ and $n$)?