Question

what is the maximum value for k for which 105!/12 power k is an integer

Answer 1

Hi, dear

Here is your answer!!

Answer:

50

Explanation:

Highest power of 3 in 105:

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

= 35 + 11 + 3 + 1

= > 50

☆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 maximum value of k to be an integer.☆