The largest natural number n such that 3 n divides 66 ! is _ _ _ _ _ _ _

Step-by-step solution

We know that, Maximum value of n for p n where p is prime divides the number a ! is given by, a p + a p 2 + a p 3 + a p 4 + . . . Since, 3 is a prime number, so we have = 66 3 + 66 3 2 + 66 3 3 + 66 3 4 + . . . = 22 + 7 + 2 + 0 = 31 So, maximum value of n is 31 .