Listfor(n, 1, 165, (99!! % 3^n) =(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508 3731656658, 508 3731656658, 5083 7316566580, 11946 7693931463, 53124 9958120761, 114892 .......etc.
I see that the first 26 powers of 3 are factors of 99!!. Therefore, the largest integer n = 26, or:
3^26 =2,541,865,828,329 which is a factor of 99!!.
Note: 99!! is the double factorial function, i.e., 99 x 97 x 95, 93 x.............x 5 x 3 x 1.