Katy has 2 packets of sugar and 12 packets of artificial sweetener. She wants to divide them into identical groups, with no packets left over, so that the groups can be distributed to some tables at the restaurant where she works. What is the greatest number of groups Katy can make?

Answer 1

To find the greatest number of identical groups that Katy can make without any packets left over from her supplies of 2 packets of sugar and 12 packets of artificial sweetener, we need to determine the greatest common divisor (GCD) of the two quantities.

1. Identify the quantities:

   • Number of sugar packets = 2
   • Number of artificial sweetener packets = 12

2. Find the GCD of 2 and 12:

   • The divisors of 2 are: 1, 2
   • The divisors of 12 are: 1, 2, 3, 4, 6, 12

   The common divisors of 2 and 12 are: 1, 2.

   The greatest common divisor is therefore 2.

3. Conclusion: The greatest number of groups Katy can make is \( \boxed{2} \).