The greatest common factor (GCF) of 35 and 77 is **7**.

### Explanation:
- **35** has the prime factorization: \( 35 = 5 \times 7 \)
- **77** has the prime factorization: \( 77 = 7 \times 11 \)

The common factor between these numbers is **7**.

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### Related Questions:
1. What is the GCF of 45 and 60?
2. How do you find the least common multiple (LCM) of 35 and 77?
3. Can two numbers have a GCF of 1? Why or why not?
4. What is the relationship between GCF and LCM?
5. How does the Euclidean algorithm work for finding GCF?

**Tip:** When the GCF is 1, the numbers are called "relatively prime" or "coprime."

Discover how to find the GCF of 35 and 77 using prime factorization. This solution explains step-by-step how the GCF is calculated with a focus on number theory concepts, suitable for students in Grades 6-8.

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