A committee organising a marathon has 42 jugs of water and 21 jugs of sports drink. The committee would like to set up a number of refreshment stations along the marathon course, with the same combination of jugs of water and jugs of sports drink at each station, with no beverages left over. What is the greatest number of refreshment stations that can be set up?

stations

To find the greatest number of refreshment stations that can be set up, we need to determine the greatest common divisor (GCD) of the number of jugs of water (42) and the number of jugs of sports drink (21). The GCD will give us the largest number of refreshment stations that can be set up with the same combination of jugs of water and sports drink, with no leftover beverages.

### Step-by-step process:

1. **List the factors of 42:**
   \[
   42 = 1, 2, 3, 6, 7, 14, 21, 42
   \]

2. **List the factors of 21:**
   \[
   21 = 1, 3, 7, 21
   \]

3. **Find the greatest common divisor (GCD):**
   The common factors of 42 and 21 are: \( 1, 3, 7, 21 \).
   The greatest of these is 21.

### Conclusion:
The greatest number of refreshment stations that can be set up is **21**.

Would you like any further details or clarification?

Here are 5 related questions you might find useful:
1. How do you find the GCD of two numbers using the Euclidean algorithm?
2. What are other practical uses of GCD in real-life situations?
3. How can you generalize this method to solve similar problems with different numbers?
4. What is the least common multiple (LCM) of 42 and 21, and how is it related to the GCD?
5. How would the number of stations change if more water or sports drink were added?

**Tip:** When finding the GCD of two numbers, listing the factors works for small numbers, but the Euclidean algorithm is faster for larger numbers.

A committee organizing a marathon has 42 jugs of water and 21 jugs of sports drink. The committee would like to set up a number of refreshment stations along the marathon course, with the same combination of jugs of water and jugs of sports drink at each station, with no beverages left over. What is the greatest number of refreshment stations that can be set up?

Discover how to use the Greatest Common Divisor (GCD) to determine the maximum number of refreshment stations for a marathon. Given 42 jugs of water and 21 jugs of sports drink, learn the step-by-step process to solve this problem, ideal for students in Grades 6-8.

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