Question

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

• A. 256
• B. 872
• C. 1504
• D. 1438

Answer 1

Answer: (D)

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 $n=1440-2=1438$