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To find the largest number which divides both 438 and 606 without leaving any remainder, we need to determine their greatest common divisor (GCD).

### Step-by-Step Solution:
1. **Prime Factorization Method:**
   - **438** can be factored as \( 438 = 2 \times 3 \times 73 \).
   - **606** can be factored as \( 606 = 2 \times 3 \times 101 \).

2. The common prime factors are **2** and **3**, so the GCD is the product of these common prime factors:
   \[
   GCD(438, 606) = 2 \times 3 = 6
   \]

Thus, the largest number that divides both 438 and 606 is **6**.

Would you like more details or have any questions?

### Related Questions:
1. What is the greatest common divisor of 540 and 810?
2. How do you find the least common multiple (LCM) of 438 and 606?
3. Can the GCD method be applied to three or more numbers?
4. What is the difference between GCD and LCM?
5. How can you find the GCD using the Euclidean algorithm?

**Tip:** The Euclidean algorithm is often a faster method for finding the GCD than prime factorization, especially for larger numbers.

Find the largest number which divides 438 and 606 without leaving any remainder.

Learn how to find the largest number that divides both 438 and 606 using the Greatest Common Divisor (GCD). This problem is solved using the prime factorization method. Suitable for students in Grades 6-8.

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