Find the number of proper factors of the number 38808. Also, find sum of all these divisors.

Explanation

The number `38808=2^(3)*3^(2)*7^(2)*11`
Hence, the total number of proper factors (excluding 1 and itself i.e., 38808)
`=(3+1)(2+1)(2+1)(1+1)-2`
`=72-2=70`
And sum of all these divisors (proper)
`=(2^(0)+2^(1)+2^(2)+2^(3))(3^(0)+3^(1)+3^(2))`
`(7^(0)+7^(1)+7^(2))(11^(0)+11^(1))-1-38808`
`=(15)(13)(57)(12)-38809`
`=133380-38809`
`=94571`