Can $\gcd(a,b)$ be called a binary operator which takes operands $a$ and $b$ and returns their greatest common divisor.
And if for some operator —say $\bigotimes$ —$(a_1\bigotimes a_2 \bigotimes ... ... \bigotimes a_{n-1} \bigotimes a_n)$ $= (a_1\bigotimes a_2...\bigotimes a_m)\bigotimes (a_{m+1}\bigotimes a_{m+2}...\bigotimes a_n)$, what is this property called?