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The problem asks to determine the remainder at the end of the 2nd step in the Euclidean algorithm used to find the greatest common divisor (GCD) of 468 and 222. The key information provided is that the divisor in the 2nd step is 24.

Let's solve this step-by-step using the Euclidean algorithm:

### Euclidean Algorithm:
1. **Step 1**: Divide 468 by 222.
   \[
   468 \div 222 = 2 \text{ (quotient)} \quad \text{remainder} = 468 - 2 \times 222 = 468 - 444 = 24
   \]
   So, the remainder after the first step is 24. We now move to the second step, where we divide the previous divisor (222) by this remainder (24).

2. **Step 2**: Divide 222 by 24.
   \[
   222 \div 24 = 9 \text{ (quotient)} \quad \text{remainder} = 222 - 9 \times 24 = 222 - 216 = 6
   \]
   So, the remainder at the end of the second step is **6**.

### Conclusion:
The remainder at the end of the second step is **6**.

Do you want further details or have any questions? 

Here are 5 related questions:
1. How is the Euclidean algorithm used to find the greatest common divisor?
2. What happens after the second step in this specific problem?
3. Can the GCD of two numbers be found by repeated subtraction?
4. What other methods can be used to find the GCD besides the Euclidean algorithm?
5. How can the Euclidean algorithm be applied to larger numbers?

**Tip**: The Euclidean algorithm is one of the most efficient methods for finding the GCD of two numbers, and it works faster than factoring the numbers directly.

Angel intenta obtener el máximo común divisor de 468 y 222 con el algoritmo de división de Euclides (ADE). En su 2° paso obtiene un divisor 24. Determina el residuo al final del 2° paso.

Solve the greatest common divisor (GCD) of 468 and 222 using the Euclidean Algorithm. In this problem, the divisor at the 2nd step is 24, and the remainder is calculated step-by-step. Suitable for Grades 9-12.

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