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  4. The sum of all the positive divisors of 180 excluding 1 and itself is

Q. The sum of all the positive divisors of $180$ excluding $1$ and itself is

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Solution:

$180 =2^{2} 3^{2} 5^{1} $
$\therefore$ the sum of all the positive divisors of $180$ excluding $1$ and itself is $=\frac{2^{3}-1}{2-1} \cdot \frac{3^{3}-1}{3-1} \cdot \frac{5^{2}-1}{5-1}-181$
$=7.13 .6-181=365$

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