Find the total number of proper factors of the number 35700. Also find sum of all these factors sum of the odd proper divisors the number of proper divisors divisible by 10 and the sum of these divisors.

Explanation

`because35700=2^(2)xx3^(1)xx5^(2)xx7^(1)xx17^(1)`
`therefore`Required number of odd proper divisors
=Total number of selections of zero 2 and any number of 3's or 5's or 7's or 17's
`=(1+1)(2+1)(1+1)(1+1)-1=23`
`therefore` The sum of odd proper divisors
`=(3^(0)+3^(1))(5^(0)+5^(1)+5^(2))(7^(0)+7^(1))(17^(0)+7^(1))-1`
`=4xx31xx8xx18-1`
`=17856-1=17855`