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Tom wants to divide 24 pencils and 36 erasers into equal groups with the most items in each group. To determine this, we need to find the greatest common divisor (GCD) of 24 and 36, which represents the largest number of items that can evenly divide into both 24 and 36.

Let's calculate the GCD:

1. **Factors of 24:** 1, 2, 3, 4, 6, 8, 12, 24
2. **Factors of 36:** 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are 1, 2, 3, 4, 6, 12. Among these, the largest is 12.

Thus, Tom should place 12 items in each group to have the most items while keeping the groups equal. This means he can create two groups of pencils (24 ÷ 12 = 2) and three groups of erasers (36 ÷ 12 = 3).

Do you need more details or have any questions on this solution? Here are some additional questions you might consider:

1. How would the answer change if Tom had a different number of pencils or erasers?
2. What is the significance of finding the GCD in practical situations?
3. How can you find the GCD using a different method, such as the Euclidean algorithm?
4. Can Tom create subgroups within these main groups? If so, what would be the configuration?
5. What are the implications of the number of groups on the distribution of items?

Tip: Finding the GCD is very useful in problems involving equal distribution or partitioning of sets into the largest possible equal subgroups.

Tom has 24 pencils and 36 erasers. He wants to divide them into equal groups with the most items in each group. How many items should be in each group?

Learn how to calculate the greatest common divisor (GCD) of 24 and 36 to determine the largest equal groups Tom can make with his pencils and erasers. This solution covers key mathematical concepts like GCD and factorization, suitable for students in Grades 6-8.

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