To answer this question you have to first convert the square ft into square inches (assuming 16 X 16 means inches). So you take 133 * 144 since 1 square ft is 12 X 12 inches and is 144 square inches. for 133 square ft, you have 19,152 square inches.
So the equation is then is:
16 * 16 * X = 19,152
X is how many 16X16 tiles you need to cover 19,152 square inches.
256X = 19,152 74.8125
So your exact answer is 74.8125 tiles and if you can't buy a portion of a tile you would need 75. However, it's unlikely 75 tiles will do it the way you want unless the room is perfectly square and in proportion of the tile (meaning a multiple of 16" in measurements). You will likely have to cut the tile to fit properly and unless you want to try and use the leftovers from the cuts you will be short.
The best way to figure how many extra over the 75 you will need is by measuring the room to get an idea on how many you will cut and throw out, if the room has any angles there will be more waste.