If we want to use a square tile of side [tex] s [/tex], we have to make sure that [tex] s [/tex] divides both 12 and 8.
The divisors of 8 are 1, 2, 4 and 8.
The divisors of 12 are 1, 2, 3, 4, 6 and 12.
So, the only common divisors are 1, 2 and 4.
Since we want the largest square tile, we choose the one with side 4.
