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The goal here is to complete the GCF-LCM Web by filling in the blank circles using the relationships between the given numbers, specifically focusing on the greatest common factor (GCF) and least common multiple (LCM). The web shows numbers 336, 21, and 3, and we’ll use these to deduce the values in the blank circles.

Let's analyze this step by step.

### Step-by-Step Solution

1. **Determine the GCF of 336 and 21**:
   - The GCF of 336 and 21 is the largest number that divides both 336 and 21.
   - Factorize each number:
     - \( 336 = 2^4 \times 3 \times 7 \)
     - \( 21 = 3 \times 7 \)
   - The common factors are 3 and 7, so the GCF of 336 and 21 is \( 3 \times 7 = 21 \).

   Therefore, **the circle between 336 and 21 should be filled with 21**.

2. **Determine the LCM of 336 and 21**:
   - The LCM of two numbers is the smallest number that both numbers divide.
   - Using the prime factors:
     - The factors for LCM are \(2^4 \times 3 \times 7\) which is 336.
   - This means the LCM of 336 and 21 is **336**.

   So, **the circle connected to 336 and 21 should also have 336** (the top circle).

3. **Determine the GCF of 21 and 3**:
   - Factorize 21 and 3:
     - \( 21 = 3 \times 7 \)
     - \( 3 = 3 \)
   - The only common factor is 3.

   Thus, **the GCF of 21 and 3 is 3**, which means the circle between them should contain 3.

4. **Determine the LCM of 21 and 3**:
   - The LCM of 21 and 3 will use the highest power of each prime factor:
     - LCM of 21 and 3 = \( 3 \times 7 = 21 \).

   Therefore, **the circle connected to 21 and 3 should contain 21**.

5. **Check Consistency with 3**:
   - Finally, we verify the consistency for the number 3 with adjacent circles.

### Final Answer

- The top circle (connected between 336 and 21) should contain **336**.
- The left circle (between 336 and 3) should contain **21**.
- The bottom circle (between 21 and 3) should contain **21**.
- The middle right circle between 21 and 3 should contain **3**.

Would you like further details on each calculation? 

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### Related Questions

1. What is the difference between GCF and LCM?
2. How do you determine the prime factorization of a large number?
3. Why do we use the highest power of each prime for finding LCM?
4. How can the GCF and LCM help in solving real-world problems?
5. What are other methods to find the LCM of two numbers?

### Tip

For quick calculations of LCM and GCF, try using their relationships with prime factors; it simplifies the process for larger numbers.

Fill each blank circle to complete the GCF-LCM Web below.

Learn how to complete a GCF-LCM web using the numbers 336, 21, and 3. This math problem involves finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM) using prime factorization. Suitable for students in Grades 6-8.

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