Atoms were considered indivisible by early philosophers and scientists. According to Democritus, Aristotle, and Maharishi Kannada, atoms were indivisible. They had no technology to prove their theory.
About a hundred years later it was proved by J.J. Thomson, who proved with his Cathode Ray Experiment that negatively charged particles were present in an atom. The presence of negatively charged particles indicated that the atom must be having positively charged particles so as to maintain its neutrality. Further experiments led to the discovery of Protons and neutrons until Neil Bohr's model got published.
Hence atom is divisible.