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!