The answer is 1024.

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2048 divided by 2 = 1024

1024 + 1024 = 2048

and then we divide 1024 by 2 and so on and our end result will be two

so to make 4 with tiles with the number two we need 2 tiles

and two make 8 from four we need another 4 so another two tiles

so basically 2 of every number is needed except the 2048 tile to make the 2048 tile