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Q.
If $n=(210)^{2}(360)(143)$, then the total number
of non trivial factors of $n$ is
TS EAMCET 2019
Solution:
For given number $n=(210)^{2}(360)(143)$, the trivial factors are 1 and $n$ itself, other factors are non-trivial.
$\because n=(2 \times 3 \times 5 \times 7)^{2}\left(2^{3} \times 3^{2} \times 5\right)(11 \times 13)$
$=2^{5} 3^{4} 5^{3} 7^{2}(11 \times 13)$
Now, total number of factors (including $l$ and $n)$
$=(5+1)(4+1)(3+1)(2+1)(1+1)(1+1)$
$=6 \times 5 \times 4 \times 3 \times 2 \times 2=1440$
So, non-trivial factors of $n=1440-2=1438$