The largest value of n , for which 40^ n divides 60! , is

Step-by-step solution

40^n = 2^ 3n 5^n . We need the highest power of 40 dividing 60! . Power of 5 in 60! = 60/5 + 60/25 = 12 + 2 = 14 . Power of 2 in 60! = 60/2 + 60/4 + 60/8 + 60/16 + 60/32 = 30 + 15 + 7 + 3 + 1 = 56 . We need n 14 and 3n 56 (i.e., n 18 ). The binding constraint is n 14 , so the largest value is n = 14 .