GCD, Greatest Common Divisor

In [here], the GCD (Greatest Common Divisor) is given in brief details. The algorithm can be implemented in both recursive and iterative forms. The recursive formula is $tex_e518e1adccbc00606ea88dc8251636c2 GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ , and it has a rough complexity $tex_4f58e175c0debc2dec03a83e5ddcff07 GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ .

The following properties may be used in other solution.

$tex_a51036a76fbe858e73b1d1f064c4cf09 GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ , if a = b

$tex_cd5d2d84fa2b6e79e5e40424c82bde6f GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ , if a and b are both even.

$tex_0a78ff501a0f0c88e2e6ed6ab8017ceb GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ if a is even and b is odd.
$tex_826ff85711d4644ffad409464c42225c GCD, Greatest Common Divisor algorithms beginner implementation math programming languages recursive$ if a and b are both odd.