Question

If N = 10800, find the(i) the number of divisors of the form 4m +2,(ii) the number of divisors which are multiple of 10(iii) the number of divisors which are multiple of 15.

Answer 1

(i) `because(4m+2)=2(2m+1)`, in any divisor of the form 4m+2, 2 should be exactly 1.
so, the number of divisors of the form
`(4m+2)=1xx(3+1)xx(2+1)=1xx4xx3=12`
(ii) `therefore`the required number of proper divisors
`=`total number of selections of atleast one 2 and one 5 from 2,2,2,2,3,3,3,4,4
`=4xx(3+1)xx2=32`.
(iii) `therefore` The required number of proper divisors
=Toal number of selection of atleast one 3 and one
5 from 2,2,2,2,3,3,3,5,5
`=(4+1)xx3xx2=30`