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Re: Divisors of a Number
by TG team - Saturday, 7 December 2013, 03:54 PM
  Hi nehasmile
To find the maximum number of days in a single year we have to look out for an year with maximum number of prime factors.
So, a few years between 50 and 100 with more than 3 prime factors are : 54,60,72,80,81,88,90 and 96.
Since the number of months can be up to 12 and number of days can be up to 31,so on a careful look we find that the only the options 60 and 90 have the maximum days.
CASE 1: 1960
2/30/60
3/20/60
4/15/60
5/12/60
6/10/60
10/6/60
12/5/60

CASE 2:1990
2/45/90(not possible)
3/30/90
5/18/90
6/15/90
9/10/90
10/9/90
Clearly,1960 is the answer.
Hope i am clearsmile