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

For given number $n=(210)^2(360)(143)$, the trivial factors are 1 and $n$ itself, other factors are non-trivial. $\begin{aligned} \because n & =(2 \times 3 \times 5 \times 7)^2\left(2^3 \times 3^2 \times 5\right)(11 \times 13) \\ & =2^5 3^4 5^3 7^2(11 \times 13)\end{aligned}$ Now, total number of factors (including 1 and $n$ ) $\begin{aligned} & =(5+1)(4+1)(3+1)(2+1)(1+1)(1+1) \\ & =6 \times 5 \times 4 \times 3 \times 2 \times 2=1440\end{aligned}$ So, non-trivial factors of $n=1440-2=1438$ Hence, option (d) is correct.