Dolores claims that she has a shortcut for finding the GCD using the Euclidean algorithm...

Dolores claims that she has a shortcut for finding the GCD using the Euclidean algorithm. She says when the remainder is large she uses a negative "remainder." For example, to find GCD (2132, 534), she divides 2132 by 534 and gets 2132 = + 530, which gives remainder 530. In such case, she writes 2132 = - 4 and claims that

Is the approach correct and if so, why?