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A new algorithm for reducing the division operation to a series of smaller divisions is introduced. Partitioning the dividend into segments, we perform divisions, shifts, and accumulations taking into account the weight of dividend bits. Each partial division can be performed by any existing division algorithm. From an algorithmic point of view, computational complexity analysis is performed in comparison with existing algorithms. From an implementation point of view, since the division can be performed by any existing divider, the designer can chose the divider which meets his specifications best. Two possible implementations of the algorithm, namely the sequential and parallel are derived, with several variations, allowing performance, cost, and cost/performance trade-offs.