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Let's work through the given parts step by step:

### A) Pick three non-prime numbers between 50 and 120. Create a factor tree for each. Write the prime factors.
Here, I'll choose three non-prime numbers: **60, 90, and 100**.

1. **60**  
   Prime factorization of 60:  
   - 60 ÷ 2 = 30  
   - 30 ÷ 2 = 15  
   - 15 ÷ 3 = 5  
   So, the prime factorization of 60 is:  
   **60 = 2 × 2 × 3 × 5**  
   Factor tree:  
   ```
        60
       /  \
      2    30
          /  \
         2    15
             /  \
            3    5
   ```

2. **90**  
   Prime factorization of 90:  
   - 90 ÷ 2 = 45  
   - 45 ÷ 3 = 15  
   - 15 ÷ 3 = 5  
   So, the prime factorization of 90 is:  
   **90 = 2 × 3 × 3 × 5**  
   Factor tree:  
   ```
        90
       /  \
      2    45
          /  \
         3    15
             /  \
            3    5
   ```

3. **100**  
   Prime factorization of 100:  
   - 100 ÷ 2 = 50  
   - 50 ÷ 2 = 25  
   - 25 ÷ 5 = 5  
   So, the prime factorization of 100 is:  
   **100 = 2 × 2 × 5 × 5**  
   Factor tree:  
   ```
        100
       /   \
      2    50
          /  \
         2    25
             /  \
            5    5
   ```

### B) Find at least two numbers that have a prime factorization with at least four unique prime numbers.
Looking for numbers between 50 and 120, the two numbers with at least four unique prime factors are:

1. **105**  
   Prime factorization:  
   - 105 ÷ 3 = 35  
   - 35 ÷ 5 = 7  
   So, the prime factorization of 105 is:  
   **105 = 3 × 5 × 7**

2. **110**  
   Prime factorization:  
   - 110 ÷ 2 = 55  
   - 55 ÷ 5 = 11  
   So, the prime factorization of 110 is:  
   **110 = 2 × 5 × 11**

### C) Can you find any numbers that have only one number in their list of prime factors? (i.e. every prime factor is 2, 3, or 5)
Yes, numbers that have only 2, 3, and 5 as their prime factors are powers of these primes or products of these primes.

1. **60** (which we already found in part A):  
   Prime factorization: **60 = 2 × 2 × 3 × 5**

2. **75**  
   Prime factorization:  
   - 75 ÷ 3 = 25  
   - 25 ÷ 5 = 5  
   So, the prime factorization of 75 is:  
   **75 = 3 × 5 × 5**

---

Would you like more details or explanations on any part?

### Related Questions:
1. What is the prime factorization of 84?
2. How can we check if a number is prime or composite?
3. Can you explain how to create a factor tree for a larger number like 144?
4. What is the difference between prime factorization and divisibility?
5. How do powers of prime numbers affect their prime factorization?

### Tip:
When performing prime factorizations, start by dividing by the smallest prime numbers (2, 3, 5, etc.) to break the number down step by step.

A) Pick three non-prime numbers between 50 and 120. Create a factor tree for each. Write the prime factors.
B) Find at least two numbers that have a prime factorization with at least four unique prime numbers.
C) Can you find any numbers that have only one number in their list of prime factors? (i.e. every prime factor is 2 or 3 or 5)

Learn how to pick non-prime numbers between 50 and 120 and create factor trees for prime factorization. This problem demonstrates prime numbers and how to identify numbers with unique prime factors, including those with prime factors of only 2, 3, or 5.

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