and 2 and write 5 and 8 above. Cross out the 4. The resulting dividend is 5884. (e) Write the divisor one step to the right of where it was originally written using empty spaces below existing crossed out digits. (f1) Dividing 588 by 594 yields 0 which is written as the new digit of the quotient. (f2) As 0 times any digit of the divisor is 0, the dividend will remain unchanged. We therefore can cross out all the digits of the divisor. (f3) We write the divisor again one space to the right (omitted) Dividing 5884 by 594 yields 9 which is written as the new digit of the quotient. 58 − 5×9 = 13 so cross out the 5 and 8 and above them write 1 and 3. Cross out the 5 of the divisor. The resulting dividend is now 1384. 138 − 9×9 = 57. Cross out 1,3, and 8 of the dividend and write 5 and 7 above. Cross out the 9 of the divisor. The resulting dividend is 574. 574 − 4×9 = 538. Cross out the 7 and 4 of the dividend and write 3 and 8 above them. Cross out the 4 of the divisor. The resulting dividend is 538. The process is done, the quotient is 109 and the remainder is 538. Other versions The above is called the cross-out version and is the most common. An erasure version exists for situations where erasure is acceptable and there is not need to keep track of the intermediate steps. This is the method used with a sand abacus. Finally, there is a printers' method that uses neither erasure or crossouts. Only the top digit in each column of the dividend is active with a zero used to denote an entirely inactive column. Modern usage Galley division was the favorite method of division with arithmeticians through the 18th century and it is thought that it fell out of use due to the lack of cancelled types in printing. It is still taught in the Moorish schools of North Africa and other parts of the Middle East. Origin Lam Lay Yong, mathematics professor of National University of Singapore, traced the origin of the galley method to the Sunzi Suanjing written about 400AD. The division described by Al-Khwarizmi in 825 was identical to the Sunzi algorithm for division. See also Group Field (algebra) Division algebra