The maximum value of n for which 40n divides 60! is equal to
11
12
13
14
14
40 = 23 × 5
Exponent of 2 in 60! = ⌊60/2⌋ + ⌊60/4⌋ + ⌊60/8⌋ + ⌊60/16⌋ + ⌊60/32⌋ + ⌊60/64⌋
= 30 + 15 + 7 + 3 + 1
= 56
Exponent of 5 in 60! = ⌊60/5⌋ + ⌊60/25⌋
= 12 + 2
= 14
Since 40 = 23 × 5
Maximum n = min(56/3 , 14)
= 14