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If $n=(210)^2(360)(143)$, then the total number of non trivial factors of $n$ is
Options:
Solution:
1134 Upvotes
Verified Answer
The correct answer is:
$1438$
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.
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.
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