Oops! I read it as 1*2*3*...*97*98*99. It isn't!
With z, say, as the product of the odd integers from 1 to 99 we have:
z→3^26*5^12*7^8*11^5*13^4*17^3*19^3*23^2*29^2*31^2*37*41*43*47*53*59*61*67*71*73*79*83*89*97
so n is 26
(and, yes, this is known as a double factorial. Thanks for pointing out my error Guest.).