Question

what is the maximum value of k for which 105!/12^k is an integer
option are 50, 49,47,48
​

Answer 1

Answer:

50

Step-by-step explanation:

Highest power of 3 in 105! =

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

= 35+11+3+1 => 50

where [ ] this bracket signifies greatest integer function.

As highest 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.