To solve this, we need to find the greatest number of identical stationery sets Jessica can make using 10 sheets of paper and 15 envelopes. Each set will contain both paper and envelopes, and there shouldn't be any paper or envelopes left over.

This requires us to find the greatest common divisor (GCD) of 10 and 15, since the GCD will tell us the largest number of identical sets she can make without any leftover items.

The factors of 10 are:
$10 = 1, 2, 5, 10$

The factors of 15 are:
$15 = 1, 3, 5, 15$

The greatest common factor is 5.

Thus, the greatest number of identical sets Jessica can make is 5.

Explanation:

• For 5 sets, Jessica will use:
  $10 \div 5 = 2$ sheets of paper per set
  $15 \div 5 = 3$ envelopes per set.

Final Answer:

Jessica can make 5 identical stationery sets.

Would you like further details on how the GCD works or have any other questions?

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Here are some related questions to explore:

1. What if Jessica had 20 sheets of paper and 30 envelopes instead?
2. How would the problem change if she had 12 sheets and 18 envelopes?
3. Can the greatest number of sets be found with other methods?
4. How does the GCD relate to real-world grouping problems?
5. How would this apply if she only wanted a set with 1 envelope and 1 sheet?

Tip: GCD problems often come up in situations involving grouping or dividing items into identical portions without leftovers.