1. **State the problem:** Find the greatest common factor (GCF) of 12 and 30, then use it to factor the sum $12 + 30$. 2. **Find the GCF:** The GCF is the largest number that divides both 12 and 30 without remainder. 3. **Prime factorization:** $$12 = 2^2 \times 3$$ $$30 = 2 \times 3 \times 5$$ 4. **Identify common factors:** Both have $2$ and $3$ in common. 5. **Calculate GCF:** $$\text{GCF} = 2 \times 3 = 6$$ 6. **Use GCF to factor the sum:** $$12 + 30 = 6 \times \frac{12}{6} + 6 \times \frac{30}{6}$$ 7. **Simplify inside the parentheses:** $$= 6 \times (\cancel{\frac{12}{6}}2 + \cancel{\frac{30}{6}}5)$$ 8. **Final factored form:** $$12 + 30 = 6 \times (2 + 5)$$ This shows how to factor a sum using the greatest common factor.