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

The number of natural number solutions to the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

If $2^{n}$ divides $16!$ and $2^{n+1}$ does not divide $16!$,then $n=$

The number of terms in the expansion of $(x+y+z)^{10}$ is

Consider the following statements:
$I$: The number of non-trivial even divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $(\alpha_1+2\alpha_3+\alpha_5)(\alpha_2+\alpha_5+1)(\alpha_4+1)-1$.
$II$: The number of non-trivial odd divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $\alpha_2+\alpha_4+\alpha_5+\alpha_2\alpha_4+\alpha_4\alpha_5$. Then:

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is