If 15^k divides 47 ! but 15^ k+1 does not divide it, then k=

Step-by-step solution

Since, 15=3 5 , so to find the exponent of 15 in 47 ! It is enough to find the exponent of 5 in 47 !. So, exponent of 5 in 47 !. = [ 47 5 ]+ [ 47 5^2 ]+ , where, [x] is greatest integer of x] . =9+1 So, required value of k is 10 . Hence, option (c) is correct.