Question

Find the total number of proper factors of the number 35700. Also find sum of all these factors

Answer 1

$35700=5^2\times 2^2\times 3^1\times 7^1\times {17}^1$
The total number of factors is equal to the total number of selections from $(5,5)$, $(2,2)$, $\left(3\right)$, $\left(7\right)$, and $\left(17\right)$, which is given by $3\times 3\times 2\times 2\times 2=72$.
These include 1 and 35700. Therefore, the number of proper divisors (excluding 1 and 35700) is $72-2=0=70$
Sum of all these factors (proper) is
$(5^0+5^1+5^2)(2^0+2^1+2^2)(3^0+3^1)(7^0+7^1)({17}^0+{17}^1)-1-35700$
$=31\times 7\times 4\times 8\times 18-1-35700=89291$