List the prime factorization, then find the GCF
1)	18 and 63
2)	32 and 40
3)	35 and 75
4)	42 and 56
5)	30, 45, and 75
6)	26, 39, and 65

Let's go through each problem step-by-step:

### 1) **Prime Factorization and GCF of 18 and 63**

- Prime factorization of **18**:  
  \( 18 = 2 \times 3^2 \)

- Prime factorization of **63**:  
  \( 63 = 3^2 \times 7 \)

- Common factors: \( 3^2 \)

- **GCF**: \( 3^2 = 9 \)

---

### 2) **Prime Factorization and GCF of 32 and 40**

- Prime factorization of **32**:  
  \( 32 = 2^5 \)

- Prime factorization of **40**:  
  \( 40 = 2^3 \times 5 \)

- Common factors: \( 2^3 \)

- **GCF**: \( 2^3 = 8 \)

---

### 3) **Prime Factorization and GCF of 35 and 75**

- Prime factorization of **35**:  
  \( 35 = 5 \times 7 \)

- Prime factorization of **75**:  
  \( 75 = 3 \times 5^2 \)

- Common factors: \( 5 \)

- **GCF**: \( 5 \)

---

### 4) **Prime Factorization and GCF of 42 and 56**

- Prime factorization of **42**:  
  \( 42 = 2 \times 3 \times 7 \)

- Prime factorization of **56**:  
  \( 56 = 2^3 \times 7 \)

- Common factors: \( 2 \times 7 \)

- **GCF**: \( 2 \times 7 = 14 \)

---

### 5) **Prime Factorization and GCF of 30, 45, and 75**

- Prime factorization of **30**:  
  \( 30 = 2 \times 3 \times 5 \)

- Prime factorization of **45**:  
  \( 45 = 3^2 \times 5 \)

- Prime factorization of **75**:  
  \( 75 = 3 \times 5^2 \)

- Common factors: \( 3 \times 5 \)

- **GCF**: \( 3 \times 5 = 15 \)

---

### 6) **Prime Factorization and GCF of 26, 39, and 65**

- Prime factorization of **26**:  
  \( 26 = 2 \times 13 \)

- Prime factorization of **39**:  
  \( 39 = 3 \times 13 \)

- Prime factorization of **65**:  
  \( 65 = 5 \times 13 \)

- Common factors: \( 13 \)

- **GCF**: \( 13 \)

---

Let me know if you want any clarifications or further explanations!

### Related Questions:
1. How do you find the least common multiple (LCM) using prime factorizations?
2. What is the relationship between the GCF and the LCM of two numbers?
3. How does the prime factorization of a number help in determining divisibility?
4. Can you explain how to find the GCF of two numbers if you only know their prime factorizations?
5. What is the GCF of 24, 36, and 48?

**Tip**: The GCF of two numbers is the product of all the prime factors they have in common, raised to the lowest power.

List the prime factorization, then find the GCF
1) 18 and 63
2) 32 and 40
3) 35 and 75
4) 42 and 56
5) 30, 45, and 75
6) 26, 39, and 65

Find the prime factorizations and GCF of pairs and groups of numbers, such as 18 and 63 or 30, 45, and 75. Learn the steps to break numbers into prime factors and determine their greatest common factor using fundamental arithmetic principles. Suitable for students in Grades 6-8.

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