Challenge - Keypad puzzle

[pinkman]

Hi everyone.
A small challenge discussed with a friend.

Any number created by a tuple of 4 digits on a square shape of 4 consecutive keys on a standard keypad share a common prime factor.

What is this common factor?
The demonstration of quite easy, you can find it once you have the common factor.

I also ask you to create a brut force algorithm, taking any tuple as defined above and finding the common factor.
Brut force might be funny because there are not a lot of combinations and the algorithm, even if brut force, has lots of possibilities of optimization.