what is the first computing machine invented ?

Before any mechanical or electronic calculating devices existed, people needed a way to keep track of numbers and perform arithmetic. The earliest such device, dating back thousands of years to ancient civilisations, is a manual counting frame consisting of a wooden or metal frame with rods holding movable beads. By sliding these beads into different positions, a user could add, subtract, and perform other simple calculations. Because it was the very first tool humans built specifically to compute, it is recognised as the first computing machine ever invented.

The other options came much later and depended on more advanced design ideas. A device made of two logarithmic scales that slide against each other to multiply and divide numbers was developed in the 17th century, long after the counting frame was already in wide use. A set of rods marked with multiplication tables, used to simplify multiplication and division by manual lookup, was invented in the early 1600s, and a mechanical device using gears to perform addition and subtraction was built shortly afterward, also in the 17th century. All three of these tools represent later refinements in calculating technology, not the original invention.

When a question asks for the "first" computing device, look for the tool with the oldest documented history rather than the most sophisticated mechanism; simplicity and antiquity, not complexity, mark the starting point of computing history.