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The Hughes Hercules H-4 by Howard Hugheswas the largest aircraft ever build (excluding aiships and the death star) . Currently the largest aircraft in operation is the Antonov An-225 Mriya, with only2 operational. Encouragingly there are rumours they are going to finish building the third prototype.
Antonove
Antonov AN-225 is the biggest aircraft in the world , actually.
That'd be the Antonov An-225 Myria