Galley division

The galley method, also known as batello or scratch method, was the primary division technique used before 1600 and remained popular for seventeen centuries. Originating in ancient China during the 1st century AD, it was later described by Al-Khwarizmi in 825. This method is distinct for creating boat-shaped figures due to its unique setup and process.

To use the galley method, one writes the dividend with a bar for the quotient, aligns the divisor below the dividend's leftmost digit, and proceeds through steps involving multiplication, subtraction, crossing out digits, and shifting the divisor. It efficiently handles division with fewer written figures compared to long division.

There are three versions: cross-out (common), erasure (used on sand abacuses), and printers' method (without erasures). The method fell out of favor in Europe due to printing challenges but is still taught in some North African and Middle Eastern schools. Its origin traces back to the Sunzi Suanjing around 400 AD, as noted by Lam Lay Yong, with Al-Khwarizmi's method mirroring this ancient Chinese algorithm.