To find the Greatest Common Factor (GCF) of 8 and 49 using a Venn diagram, we need to follow these steps:

### 1. Prime Factorization
Start by breaking both numbers into their prime factors.

- Prime factorization of 8:
  \[
  8 = 2 \times 2 \times 2 = 2^3
  \]

- Prime factorization of 49:
  \[
  49 = 7 \times 7 = 7^2
  \]

### 2. Venn Diagram Representation
Now we place the prime factors in two circles of a Venn diagram:
- One circle represents the factors of 8: \(2^3\).
- The other circle represents the factors of 49: \(7^2\).

#### Since the prime factorizations share no common prime factors, there is **no overlap** between the circles.

### 3. Finding the GCF
The GCF is the product of the prime factors in the overlapping region of the Venn diagram. Because there are no common prime factors between 8 and 49, their GCF is:

\[
\text{GCF} = 1
\]

### Visual Summary:
- One circle has 2, 2, 2 (for 8).
- The other circle has 7, 7 (for 49).
- No common factors in the overlapping region, so the GCF = 1.

Would you like more details or further clarification on any steps?

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Here are five related questions to expand your understanding:
1. How would you use the Venn diagram to find the GCF of 12 and 18?
2. What is the Least Common Multiple (LCM) of 8 and 49, and how would a Venn diagram help?
3. Can you find the GCF of three numbers using a Venn diagram?
4. What is the GCF of 8 and 64, and how does it differ from 8 and 49?
5. Why is the GCF of two prime numbers always 1?

**Tip**: Prime factorization is a key method for finding both the GCF and LCM of numbers.

Learn how to find the Greatest Common Factor (GCF) of 8 and 49 using a Venn diagram. This tutorial covers prime factorization and visually shows why the GCF is 1. Ideal for students in Grades 6-8.

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