1. **State the problem:** Find factors of 8 and 20 such that when multiplied and then added, the sum is 14. 2. **Identify factors:** - Factors of 8: 1, 2, 4, 8 - Factors of 20: 1, 2, 4, 5, 10, 20 3. **Set up the equation:** Let the factors be $a$ (from 8) and $b$ (from 20). We want $a \times b + a + b = 14$. 4. **Rewrite the equation:** $$a \times b + a + b = 14$$ Add 1 to both sides: $$a \times b + a + b + 1 = 15$$ Factor the left side as: $$(a + 1)(b + 1) = 15$$ 5. **Find pairs $(a+1, b+1)$ that multiply to 15:** Possible factor pairs of 15 are (1,15), (3,5), (5,3), (15,1). 6. **Check which pairs correspond to valid $a$ and $b$:** - If $a+1=3$ and $b+1=5$, then $a=2$ and $b=4$. - Check if $a=2$ is a factor of 8 (yes) and $b=4$ is a factor of 20 (yes). 7. **Verify the sum:** $$2 \times 4 + 2 + 4 = 8 + 6 = 14$$ **Answer:** The factors are $2$ (from 8) and $4$ (from 20).