Question

What is the maximum value of *for which 105/12*is an integer?

Answer 1

50

Highest power of 3 in 105! =

[105/3^1]+[105/3^2]+[105/3^3]+[105/3^4]

= 35+11+3+1 => 50

As heighest power of 2 will be greater in 105! We don't need to calculate this for all the prime factors of 12 to get the maximum value of k for 105!/12^k to be an integer