It looks like you provided a sequence of numbers: 9, 12, 18, and 105. Let’s analyze this set in terms of factors, greatest common divisors (GCD), and potential relationships.

1. **Prime Factorization:**
   - 9 = \(3^2\)
   - 12 = \(2^2 \times 3\)
   - 18 = \(2 \times 3^2\)
   - 105 = \(3 \times 5 \times 7\)

2. **GCD (Greatest Common Divisor):**
   - The common factor among these numbers is 3. So, the GCD of 9, 12, 18, and 105 is 3.

3. **LCM (Least Common Multiple):**
   - The LCM is found by taking the highest powers of all prime factors:
     \[
     \text{LCM} = 2^2 \times 3^2 \times 5 \times 7 = 1260
     \]

4. **General Pattern:**
   - The first three numbers (9, 12, and 18) have a common factor of 3, but 105 introduces new prime factors (5 and 7), which breaks the simpler pattern.

Would you like more details or have any specific questions?

### 5 Related Questions:
1. How do you find the greatest common divisor (GCD) of multiple numbers?
2. How can you calculate the least common multiple (LCM) for any set of numbers?
3. What are the steps for performing prime factorization?
4. Why is the GCD of these numbers 3, and how does this affect their divisibility?
5. How can patterns in numbers help identify relationships in a sequence?

**Tip:** Prime factorization is useful for both GCD and LCM calculations—mastering it can simplify many math problems!

Discover the prime factorizations of 9, 12, 18, and 105. Learn how to calculate their greatest common divisor (GCD) and least common multiple (LCM) with step-by-step explanations. Perfect for students in Grades 6-8 studying prime factors, GCD, and LCM.

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