3. What are the factors of 12 ? Use an area model to find the factors. \( 1,2,3,4,6,12 \) \( 1,3,6,12 \) \( 1,3,9,12 \) \( 2,4,6,8,12 \)

To find the factors of 12, we start by determining all the pairs of numbers that multiply to give 12. 1. Consider the factor pair: \[ 1 \times 12 = 12 \] So, both \(1\) and \(12\) are factors. 2. Next, find another pair: \[ 2 \times 6 = 12 \] So, \(2\) and \(6\) are factors. 3. Then, check: \[ 3 \times 4 = 12 \] Thus, \(3\) and \(4\) are factors. When we list all these factors, we have: \[ 1, 2, 3, 4, 6, 12 \] An area model can help visualize this concept. Imagine a rectangle where the area (the total number of unit squares) is 12. We can partition the rectangle in different ways corresponding to the factor pairs: - A rectangle with dimensions \(1 \times 12\) (1 row and 12 columns). - A rectangle with dimensions \(2 \times 6\) (2 rows and 6 columns). - A rectangle with dimensions \(3 \times 4\) (3 rows and 4 columns). Each factor pair provides a different way to create the area of the rectangle, and by combining all unique factors from these pairs, we obtain: \[ 1, 2, 3, 4, 6, 12 \] Therefore, the correct answer is: \[ 1,2,3,4,6,12 \]