To find the **Greatest Common Factor (GCF)** and the **Least Common Multiple (LCM)** of 70 and 98, we can use the following steps:

### 1. Find the Prime Factorizations:
- 70:  
  \( 70 = 2 \times 5 \times 7 \)
- 98:  
  \( 98 = 2 \times 7 \times 7 \)

### 2. Calculate the GCF:
The **GCF** is found by taking the product of the common prime factors with the lowest powers in both factorizations:
- Common factors: \( 2 \) and \( 7 \)
- GCF: \( 2 \times 7 = 14 \)

### 3. Calculate the LCM:
The **LCM** is found by taking the product of all the prime factors, using the highest powers from either factorization:
- LCM: \( 2 \times 5 \times 7 \times 7 = 490 \)

### Conclusion:
- **GCF of 70 and 98** = 14
- **LCM of 70 and 98** = 490

Would you like more details or clarifications? Here are 5 related questions to deepen your understanding:

1. How can the Euclidean algorithm be used to find the GCF of 70 and 98?
2. Why is the LCM important when working with fractions?
3. How can the GCF help simplify fractions with these two numbers?
4. Can you find the GCF and LCM of more than two numbers? How?
5. How does the prime factorization method compare to using divisibility rules for finding GCF and LCM?

**Tip:** The LCM of two numbers is always a multiple of their GCF.

Learn how to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 70 and 98 using prime factorization. This step-by-step guide covers number theory concepts such as prime factorization, and shows how to calculate GCF and LCM with detailed explanations. Suitable for students in Grades 6-8.

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