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When there is no division circuit available, the arithmetical function of division is normally performed by a library subroutine. The library subroutine normally allows both the divisor and the dividend to be variables, and requires the execution of hundreds of assembly instructions. This correspondence provides a fast algorithm for performing the integer division of a variable by a predetermined divisor. Based upon this algorithm, an efficient division routine has been constructed for each odd divisor up to 55. These routines may be implemented in assembly languages, in microcodes, and in special-purpose circuits.