A 16 X 16 inch tile encompasses 256 inches (16 multiplied by 16). A square foot = 12 inches X 12 inches. So 350 square feet would be 350 multiplied by 12 multiplied by 12 = 50,400 inches. So 50,400 inches (350 square feet) divided by 256 inches (16 X 16 inch tile) = 196.875 which would mean you would need approximately 197 tiles. This is only the math portion of your question, however you may need more than that to account for errors and tile cuts to fit the dimensions of your room.
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Tiles that are two feet on a side cover 4 square feet. 378 of them cover 1512 square feet.
If the tiles are 1 foot squares, it will take 1,650 of them to cover 1,650 square feet. If the tiles are 16 inch square (1-1/3 square feet, each), then it would take 1,238 tiles.
I'm going to assume that the tiles are square inches, rather than square feet. But they can be converted to 3 square feet, which means 70 of them would cover the space if it were perfectly rectangular. Get 80 to be safe.
76.6 tiles
67 tiles.