Final answer:
Jerry can make only one group of cards with the given numbers of baseball, basketball, and hockey cards, since he cannot divide the hockey cards evenly and therefore must use the greatest common factor that isn't a factor of the number of hockey cards, which is 1.
Step-by-step explanation:
When trying to form groups with the same number of baseball cards, basketball cards, and hockey cards, we need to look for a common factor. Jerry has 14 baseball cards, 16 basketball cards, and 30 hockey cards. However, we are told that he can't divide the number of hockey cards equally among the groups. This means we are looking for the greatest common factor (GCF) of 14 and 16 that isn't a factor of 30 as well. The factors of 14 are 1, 2, 7, and 14. The factors of 16 are 1, 2, 4, 8, and 16. The common factors are 1 and 2. However, factor 2 is also a factor of 30, thus, the highest factor that can be used to form groups, given the condition, is 1.
Hence, Jerry can make only one group of cards with 14 baseball, 16 basketball, and 30 hockey cards without dividing the number of hockey cards equally.