If $n={\left(210\right)}^2\left(360\right)\left(143\right)$ then the total numbers of non trivial factors of n is

$\mathrm{n}={\left(210\right)}^2 \left(360\right) \left(143\right)$

$\mathrm{n}=\left(7^2\times 3^2\times 2^2\times 5^2\right)\times \left(2^3\times 5^1\times 3^2\right) \left(11\times 13\right)$

$n =2^5\times 3^4\times 5^3\times 7^2\times 11\times 13$

$\begin{array}{rcl}\mathrm{Total} \mathrm{no}. \mathrm{of} \mathrm{divisors} & =& (5+1)(4+1)(3+1)(2+1)(1+1)(1+1)\\ & =& 6\left(5\right)4 \left(3\right) \left(2\right)2\\ & =& 1440\end{array}$

$\begin{array}{rcl}\mathrm{No}. \mathrm{of} \mathrm{non} \mathrm{trivial} \mathrm{divisors}& =& 1440-2\\ & =& 1438\end{array}$