Factor pairs are two numbers that multiply together to give a specific product. For example, 2 and 3 are a factor pair of 6 because 2 times 3 equals 6. We can visualize this using rectangles where the length and width represent the factors and the area represents the product.
To find all factor pairs systematically, we start testing divisors from 1 upward. For each number, we divide our target number by it. If the result is a whole number, we've found a factor. We only need to check up to the square root of the number because factors come in pairs.
Now let's find all factors of 24. We test each number from 1 to 24 by dividing 24 by it. Green results show whole numbers, meaning we found factors. Red results show decimals, meaning those numbers are not factors. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Now we pair the factors to form factor pairs. We match the smallest factor with the largest, then the next smallest with the next largest, and so on. The factor pairs of 24 are: (1, 24), (2, 12), (3, 8), and (4, 6). Each pair multiplies to give 24.
We can visually verify our factor pairs using rectangular arrays. Each factor pair represents the dimensions of a rectangle with area 24. For example, a 1 by 24 rectangle, a 2 by 12 rectangle, a 3 by 8 rectangle, and a 4 by 6 rectangle all have an area of 24 squares. These visual models confirm our mathematical calculations.
In summary, the factor pairs of 24 are (1, 24), (2, 12), (3, 8), and (4, 6). We verified each pair by multiplication, confirming they all equal 24. This gives us a total of 4 distinct factor pairs. Understanding factor pairs is useful in many areas of mathematics, such as finding dimensions of rectangles with a given area, simplifying fractions, and solving algebraic equations.