The set of common factors of $a$ and $b$ is the same as the set of factors of $\text{GCD}(a, b)$

The $\text{GCD}(a, b)$ is always the sum of the common factors

$\text{GCD}(a, b)$ has no factors

The number of factors of $\text{GCD}(a, b)$ is always larger than the number of common factors