, Volume 5, Issue 1, pp 1–10

An improved parallel algorithm for integer GCD


  • Benny Chor
    • Laboratory for Computer ScienceMassachusetts Institute of Technology
  • Oded Goldreich
    • Laboratory for Computer ScienceMassachusetts Institute of Technology

DOI: 10.1007/BF01840374

Cite this article as:
Chor, B. & Goldreich, O. Algorithmica (1990) 5: 1. doi:10.1007/BF01840374


We present a simple parallel algorithm for computing the greatest common divisor (gcd) of twon-bit integers in the Common version of the CRCW model of computation. The run-time of the algorithm in terms of bit operations isO(n/logn), usingn1+ɛ processors, where ɛ is any positive constant. This improves on the algorithm of Kannan, Miller, and Rudolph, the only sublinear algorithm known previously, both in run time and in number of processors; they requireO(n log logn/logn),n2 log2n, respectively, in the same CRCW model.

We give an alternative implementation of our algorithm in the CREW model. Its run-time isO(n log logn/logn), usingn1+ɛ processors. Both implementations can be modified to yield the extended gcd, within the same complexity bounds.

Key words

Greatest common divisorParallel algorithms

Copyright information

© Springer-Verlag New York Inc. 1990