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Reference.org
Binary GCD algorithm
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<p>The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the <a href="/facts/Greatest_common_divisor/kNFvBuKl">greatest common divisor</a> (GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional <a href="/facts/Euclidean_algorithm/wApql29c">Euclidean algorithm</a>; it replaces division with <a href="/facts/Arithmetic_shift/xL4SXdpw">arithmetic shifts</a>, comparisons, and subtraction. </p><p>Although the algorithm in its contemporary form was first published by the physicist and programmer Josef Stein in 1967, it was known by the 2nd century BCE, in ancient China. </p>