An elementary school teacher wants to divide all the pencils and erasers donation into equal groups. There were 72 pencils and 88 erasers donated. Each group must have the same number of pencils. Each group must have the same number of the racers the teacher will make as many groups as possible, which choice describes each group that the principal will make.

To solve this, the teacher wants to divide 72 pencils and 88 erasers into the maximum number of equal groups. Each group must have the same number of pencils and the same number of erasers. This requires finding the greatest common divisor (GCD) of 72 and 88, which will determine the maximum number of equal groups.

### Step 1: Find the GCD of 72 and 88
We can use the prime factorization or the Euclidean algorithm to find the GCD.

#### Prime factorization:
- 72 = 2³ × 3²
- 88 = 2³ × 11

The only common prime factor is \(2³\), which gives the GCD as 8.

### Step 2: Divide by the GCD
- Number of pencils per group: \( \frac{72}{8} = 9 \)
- Number of erasers per group: \( \frac{88}{8} = 11 \)

### Conclusion:
The teacher will make 8 groups, and each group will have 9 pencils and 11 erasers.

Would you like further details or have any questions?

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Here are 5 related questions:
1. What if the donation had 84 pencils and 98 erasers?
2. How would you distribute items with no common divisor?
3. How can you apply the GCD in real-life situations other than dividing objects?
4. What if the teacher wanted fewer groups instead of the maximum number?
5. How does the Euclidean algorithm work to find the GCD?

**Tip**: Understanding how to find the GCD can help solve many problems involving equal distribution and simplifying ratios!

Learn how to divide 72 pencils and 88 erasers into the maximum number of equal groups using the Greatest Common Divisor (GCD). This problem involves key concepts like division, prime factorization, and the Euclidean algorithm. Perfect for students in Grades 4-6.

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