The binary GCD algorithm is an efficient alternative that substitutes division with faster operations by exploiting the binary representation used by computers., pp. 321–323 However, this alternative also scales like O(h²). It is generally faster than the Euclidean algorithm on real computers, even though it scales in the same way., pp. 77–79, 81–85, 425–431 Additional efficiency can be gleaned by examining only the leading digits of the two numbers a and b., p. 328 The binary algorithm can be extended to other bases (k-ary algorithms), with up to fivefold increases in speed. Lehmer's GCD algorithm uses the same general principle as the binary algorithm to speed up GCD computations in arbitrary bases.
The binary GCD algorithm is an efficient alternative that substitutes division with faster operations by exploiting the binary representation used by computers., pp. 321–323 However, this alternative also scales like O(h²). It is generally faster than the Euclidean algorithm on real computers, even though it scales in the same way., pp. 77–79, 81–85, 425–431 Additional efficiency can be gleaned by examining only the leading digits of the two numbers a and b, p. 328 The binary algorithm can be extended to other bases (k-ary algorithms), with up to fivefold increases in speed. Lehmer's GCD algorithm uses the same general principle as the binary algorit.hm to speed up GCD computations in arbitrary bases.