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I see that you've uploaded an image with a set of GCF (Greatest Common Factor) problems. I'll go ahead and solve each of them for you.

Here are the problems, and I'll provide the GCF for each pair of numbers:

1. **14, 60**
   - Prime factors of 14: \( 2, 7 \)
   - Prime factors of 60: \( 2^2, 3, 5 \)
   - GCF = \( 2 \)

2. **16, 32**
   - Prime factors of 16: \( 2^4 \)
   - Prime factors of 32: \( 2^5 \)
   - GCF = \( 2^4 = 16 \)

3. **20, 30**
   - Prime factors of 20: \( 2^2, 5 \)
   - Prime factors of 30: \( 2, 3, 5 \)
   - GCF = \( 2 \times 5 = 10 \)

4. **50, 64**
   - Prime factors of 50: \( 2, 5^2 \)
   - Prime factors of 64: \( 2^6 \)
   - GCF = \( 2 \)

5. **8, 12**
   - Prime factors of 8: \( 2^3 \)
   - Prime factors of 12: \( 2^2, 3 \)
   - GCF = \( 2^2 = 4 \)

6. **30, 42**
   - Prime factors of 30: \( 2, 3, 5 \)
   - Prime factors of 42: \( 2, 3, 7 \)
   - GCF = \( 2 \times 3 = 6 \)

7. **10, 15**
   - Prime factors of 10: \( 2, 5 \)
   - Prime factors of 15: \( 3, 5 \)
   - GCF = \( 5 \)

8. **25, 75**
   - Prime factors of 25: \( 5^2 \)
   - Prime factors of 75: \( 3, 5^2 \)
   - GCF = \( 5^2 = 25 \)

### Summary of GCFs:
1. GCF(14, 60) = 2  
2. GCF(16, 32) = 16  
3. GCF(20, 30) = 10  
4. GCF(50, 64) = 2  
5. GCF(8, 12) = 4  
6. GCF(30, 42) = 6  
7. GCF(10, 15) = 5  
8. GCF(25, 75) = 25  

Would you like any additional explanations for these? 

Here are some relative questions for you to expand on:

1. How do you find the prime factors of a number?
2. Can the GCF of two numbers ever be greater than one of the numbers?
3. Why is finding the GCF useful in simplifying fractions?
4. How does the Euclidean algorithm help in finding the GCF?
5. What is the relationship between GCF and LCM (Least Common Multiple)?

**Tip:** Always break numbers down into their prime factors for an easier and more accurate calculation of the GCF.

Solve the GCF problems for the following pairs of numbers: (14,60), (16,32), (20,30), (50,64), (8,12), (30,42), (10,15), (25,75).

Learn how to find the Greatest Common Factor (GCF) for pairs of numbers such as (14,60), (16,32), and others. Using prime factorization, this method is perfect for students in grades 6-8 looking to strengthen their number theory skills.

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