If 26!= _n 8^k , where k and n are positive integers, then what is the maximum value of k ?

Step-by-step solution

26!=n 8^k=n 2^ 3 k Maximum power of 2 aligned & = [ 26 2 ]+ [ 26 4 ]+ [ 26 8 ]+ [ 26 16 ] & =13+6+3+1=23 aligned But power of 2=3 k Maximum value of 3 k=21 Hence, the maximum value of k=7 .