- Jackie's rectangle shows that 7 is a factor of 21. Use the number sentence you wrote for Question 2 to name another factor of 21.
- Use your number sentence in Question 3 to name two factors of 32.
- Did you find two more factors in Question 4? What are they?
Finding Factors
The factors of a number must be whole numbers that can be multiplied to get the number. For example, 3 8 = 24, so 3 and 8 are factors of 24. Three and eight are whole numbers. All the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, because we can multiply pairs of numbers to get 24 in the following ways: 1 24, 2 12, 3 8, and 4 6.
The factors of a number can also be described as the whole numbers that divide the number evenly. 2 is a factor of 24 because 24 ÷ 2 = 12. But 5 is not a factor of 24 because 24 ÷ 5 = 4.8, and 4.8 is not a whole number.
The number sentence 24 = 3 8 tells us:
- 24 is a multiple of both 3 and 8.
- 3 and 8 are both factors of 24.
The factors of a number tell us which numbers of rows are possible in rectangles made with that number of tiles. Jacob couldn't make a rectangle with 5 rows and 24 tiles because 5 is not a factor of 24.
- Is it possible to make a rectangle with 24 tiles and 6 rows? If so, how many tiles will be in each row? Use your calculator to check.
- Is it possible to make a rectangle with 24 tiles and 7 rows? Use your calculator to check. Explain.