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### Problem 6: 
**What is the greatest common factor of 430 and 1,272?**

The greatest common factor (GCF) is the largest number that divides both numbers evenly.
- The prime factors of 430 are: \( 2 \times 5 \times 43 \)
- The prime factors of 1,272 are: \( 2^2 \times 3 \times 53 \)

The only common factor is \( 2 \), so the GCF is **2**.

**Answer: G (2)**

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### Problem 7:
**11 is the greatest common factor of all the following pairs of numbers except:**
- \( A. \ 11 \text{ and } 22 \)
- \( B. \ 22 \text{ and } 44 \)
- \( C. \ 77 \text{ and } 187 \)
- \( D. \ 132 \text{ and } 143 \)
- \( E. \ 242 \text{ and } 473 \)

We find the GCF for each pair:
- GCF(11, 22) = 11
- GCF(22, 44) = 22
- GCF(77, 187) = 11
- GCF(132, 143) = 1 (This is the exception)
- GCF(242, 473) = 11

**Answer: D**

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### Problem 8:
**What is the least common multiple (LCM) of 100 and 250?**

The least common multiple is the smallest number divisible by both 100 and 250.
- Prime factors of 100: \( 2^2 \times 5^2 \)
- Prime factors of 250: \( 2 \times 5^3 \)

LCM = \( 2^2 \times 5^3 = 500 \)

**Answer: K (500)**

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### Problem 9:
**What is the greatest common factor (GCF) of 72 and 108?**

The prime factorization:
- 72 = \( 2^3 \times 3^2 \)
- 108 = \( 2^2 \times 3^3 \)

The common factors are \( 2^2 \times 3^2 = 36 \).

**Answer: E (36)**

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### Problem 10:
**What is the greatest common factor (GCF) of 28 and 56?**

The prime factorization:
- 28 = \( 2^2 \times 7 \)
- 56 = \( 2^3 \times 7 \)

The common factors are \( 2^2 \times 7 = 28 \).

**Answer: J (28)**

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Would you like more details or explanations for any of these steps? 

Here are 5 related questions:
1. How is the least common multiple different from the greatest common factor?
2. Can two numbers have more than one common factor?
3. Why is prime factorization useful for finding the GCF and LCM?
4. How do you find the GCF of large numbers without prime factorization?
5. What happens if two numbers have no common factors?

**Tip:** When finding the greatest common factor, using prime factorization helps simplify the process for larger numbers.

What is the greatest common factor of 430 and 1,272? 11 is the greatest common factor of all the following pairs of numbers except: A. 11 and 22 B. 22 and 44 C. 77 and 187 D. 132 and 143 E. 242 and 473. What is the least common multiple of 100 and 250? What is the greatest common factor of 72 and 108? What is the greatest common factor of 28 and 56?

Learn how to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) with examples like GCF of 430 and 1,272, LCM of 100 and 250, and more. This guide covers prime factorization methods and is suitable for students in Grades 6-8.

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