Challenge - Keypad puzzle

[John Keith]

Assuming here that you meant permutations, it seems that the two groups on the left side of the keypad, { 1 2 4 5 } and { 4 5 7 8 } share the same common factor.

However, the two groups on the right hand side, { 2 3 5 6 } and { 5 6 8 9 } do not share the same common factor nor any others.

Maybe I am missing something?

Another amusing observation: the "almost square" formed by the digits { 0 1 2 } on the lower left (ignoring the decimal point) share the same common factor as the other two groups on the left side.