How many of the factorials from 1! to 100! are divisible by \(60\)?
Note that 1 * 2 * 3 * 4 * 5 = 5! = 120 = (60 * 2)
Then 6! = 5! * 6 = (60 * 2) * 6 = 60 (12)
And every factorial from 7 to 100 will contain 5! = 60 * 2
So from 1! to 100! we will have
100 - 5 + 1 = 96 factorials that are divisible by 60
