For number N=35700, find
(i) number of divisors
(ii) number of proper divisors
(iii) number of even divisors
(iv) number of odd divisors
(v) sum of all divisors

Explanation

`N=35700=5^(2)xx2^(2)xx3^(1)xx7^(1)xx17^(1)`
(i) Number of divisors
`=(2+1)xx(2+1)xx(1+1)xx(1+1)xx(1+1)`
`=3xx3xx2xx2xx2`
=72
(ii) Number of proper divisors =72-2=70
(iii) Number of even divisors `=3xx2xx2xx2xx2` (as 2 must occur at least once)
=48
(iv) Number of odd divisors =72-48=24
(v) Sum of divisors `=(5^(@)+5^(1)+5^(2))(2^(@)+2^(1)+2^(2))(3^(@)+3^(1))(7^(@)+7^(1))(17^(@)+17^(1))`
`=31xx7xx4xx8xx18`
=124992