List the factors of each number. Find the largest number that appears in both lists.
Factors of 12: 12, 6, 4, 3, 2, 1
Factors of 15: 15, 5, 3, 1
The highest common factor of 12 and 15 is 3. That means that the greatest possible number of sales kits is 3, because 12 samples of tile could be split into 3 kits with 4 samples of tile each and 15 samples of carpet could be split into 3 kits with 5 samples of carpet each.
The greatest number of sales kits Adam can prepare is 3.