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The problem asks to find the largest number of students that can be arranged evenly at each desk given that there are **42 students** and **54 desks** in a classroom. 

To solve this, we need to determine the greatest common divisor (GCD) of 42 and 54. The GCD will give us the largest number of students that can be evenly distributed at each desk.

### Steps:
1. Find the prime factorizations of both 42 and 54:
   - \( 42 = 2 \times 3 \times 7 \)
   - \( 54 = 2 \times 3^3 \)
   
2. The common factors are \( 2 \times 3 = 6 \).

So, the GCD of 42 and 54 is 6. 

Thus, the largest number of students that can be evenly arranged at each desk is **6**.

Would you like further clarification on this or additional details?

Here are some related questions for further practice:
1. What is the least common multiple (LCM) of 42 and 54?
2. If there were 84 students and 72 desks, what would be the largest number of students per desk?
3. How many groups of 6 students can be formed from 42 students?
4. If 7 desks are added, how does that affect the largest number of students per desk?
5. Can there be a situation where one desk has more students than another in this problem?

**Tip**: Finding the GCD is useful for optimizing distribution problems in many real-life applications.

There are 42 students and 54 desks in a classroom. What is the largest number of students that can be arranged evenly at each desk?

Learn how to determine the largest number of students that can be evenly arranged at each desk given 42 students and 54 desks in a classroom. This solution uses the GCD method to divide students equally. Suitable for students in Grades 6-8.

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