The answer will depend on the dimensions used for the tiles. 16*16 WHAT? square inches, square centimetres, square something else? Since you have not bothered to provide this key bit of information, I cannot provide a more useful answer.
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700 sq ft = 700*12*12 = 100800 sq inches 16*16 sq inches = 256 sq inches So number of tiles = 100800/256 = 393.75 If this is for real, rather than a maths sum, allow for the fact that the shape you are tiling may not correspond to a whole number of tiles along its length or breadth and also for breakages.
18" x 18" = 1.5 ft x 1.5 ft = 2.25 sq ft. Number of tiles required = 700/2.25 = 311.11... so 312 tiles are required. That is the mathematical answer to the question. In real life, you will need to make an allowance for your skill level and the awkwardness of the shape being tiled - which will affect the proportion of offcuts that can be used.
It would take approximately 311 tiles plus 5% to 10% waste depending on how you lay your floor out and how many cuts you will have.
22 will cover the space. Get 25 for any odd shapes.
It will cover an area of approximately 408.33 square feet.