 The final \(A = B\) yields the greatest common divisor of the numbers \(A\) and \(B\) that you started with. For instance, suppose you start the algorithm with \(A = 20\), \(B = 12\). Then in the first step, \(A\) gets replaced by \(20 - 12 = 8\), so \(8\) becomes the new \(A\). In the second step, \(B\) gets replaced by \(12 - 8 = 4\), so \(4\) becomes the new \(B\). In the third step, \(A\) gets replaced by \(8 - 4 = 4\), so \(4\) becomes the new \(A\) and the two numbers \(A\) and \(B\) have become equal. The algorithm yields \(4\) as the GCD of \(20\) and \(12\).