here goes the technical solution...

240 = 2⁴3¹ 5¹

we want factors of the form 2(2m+1) so we want odd multiples of 2....

so out of four powers we want only one 2.....rest to be choosen frm 3 and 5....

i have two objects 3 and five...total no of selections that i can make....

so total no of ways = (exp of 3 +1)(exp of 5 +1)= 2*2 =4

rate if useful.....