No way to determine, they are present in different forms in many different civilizations and probably had prehistoric origins.
The abacus is simply a highly portable form of the much earlier counting board or counting table, that used pebbles or clay counters in grooves on a wood board or a table covered with a thin layer of sand.
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The abacus was invented to help people calculate.
The abacus was invented before cameras and so no photograph exists.
The abacus was invented by the Sumerians in 2,700 BCE, not in 1642 ACE