Also, when stretching analogies far enough, one could argue that the GCD serves a similar purpose in number theory like the inner product in linear algebra. :-)

Also, when stretching analogies far enough, one could argue that the GCD serves a similar purpose in number theory like the inner product in linear algebra. :-) However, I think the real reason is the notation of GCD as an Ideal generated over two elements of a Ring, as described in the other reply: https://news.ycombinator.com/item?id=6090688 https://news.ycombinator.com/item?id=6090688