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Find the number of proper factors of the...

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

Text Solution

Verified by Experts

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`
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