1. **State the problem:** Nancy has 20 tulips and wants to arrange them in arrays where each row has the same number of tulips and each column has the same number of tulips, using all 20 tulips. 2. **Formula and rule:** To form an array using all tulips, the total number of tulips must equal the product of the number of rows and columns: $$\text{rows} \times \text{columns} = 20$$ 3. **Check each proposed array:** - 1 row of 20 tulips: $$1 \times 20 = 20$$ (uses all tulips) ✔️ - 3 rows of 8 tulips: $$3 \times 8 = 24$$ (more than 20, not possible) ❌ - 5 rows of 4 tulips: $$5 \times 4 = 20$$ (uses all tulips) ✔️ - 6 rows of 4 tulips: $$6 \times 4 = 24$$ (more than 20, not possible) ❌ - 20 rows of 1 tulip: $$20 \times 1 = 20$$ (uses all tulips) ✔️ - 10 rows of 2 tulips: $$10 \times 2 = 20$$ (uses all tulips) ✔️ 4. **Summary:** Arrays that use all 20 tulips are: - 1 row of 20 tulips - 5 rows of 4 tulips - 20 rows of 1 tulip - 10 rows of 2 tulips Arrays with 3 rows of 8 tulips or 6 rows of 4 tulips are not possible because they require more than 20 tulips. **Final answer:** Nancy can make arrays with 1x20, 5x4, 20x1, and 10x2 tulips using all 20 tulips.