Given two nonzero integers $a$ and $b$, what can be said about their common divisor based on the following equation?

Question

The problem is the following:

Let $a$ and $b$ be non-zero integers. Let there be two integers $s$ and $t$ such that $sa + tb = 6$.

What can be said about the common divisors of $a$ and $b$ based on this equality?

If someone could help me out with this problem, I would appreciate it very much. I have tried solving it and have made no viable progress. My guess is that the problem is somewhat simple and most importantly easy, but I am missing that starting point.

Answer 1

Welll if $d|a$ then $d|sa$ and if $d|b$ then $d|tb$. And anything that divides $sa$ and also divides $tb$ will divide the sum of $sa$ and $tb$ so......