1. **State the problem:** (a) Find the greatest common factor (GCF) of 2 and 6. 2. **Recall the definition:** The greatest common factor of two numbers is the largest number that divides both without leaving a remainder. 3. **List factors:** - Factors of 2: 1, 2 - Factors of 6: 1, 2, 3, 6 4. **Find common factors:** Common factors of 2 and 6 are 1 and 2. 5. **Choose the greatest:** The greatest common factor is $2$. 6. **Use the GCF to factor $2 + 6$:** We write $2 + 6$ as $\text{GCF} \times (\text{something})$. 7. **Divide each term by the GCF:** $$2 + 6 = 2 \times 1 + 2 \times 3$$ 8. **Factor out the GCF:** $$2 + 6 = 2 \times (1 + 3)$$ **Final answers:** - GCF = 2 - $2 + 6 = 2 \times (1 + 3)$