A landscaper is choosing a compost bin. He wants it to hold exactly 12 cubic feet of compost. Using whole numbers only, how many different sizes can he choose from?
To find the different sizes of compost bins the landscaper can choose from, we need to consider the factors of 12. The factors of 12 are the numbers that divide 12 without leaving a remainder.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
Now, let's determine the different sizes the landscaper can choose from.
If the landscaper wants the bin to hold exactly 12 cubic feet of compost, here are the different sizes he can choose from:
- Size 1: A compost bin that has a volume of 1 cubic foot. (1 x 1 x 1)
- Size 2: A compost bin that has a volume of 2 cubic feet. (2 x 1 x 1)
- Size 3: A compost bin that has a volume of 3 cubic feet. (3 x 1 x 1)
- Size 4: A compost bin that has a volume of 4 cubic feet. (2 x 2 x 1)
- Size 6: A compost bin that has a volume of 6 cubic feet. (2 x 3 x 1)
- Size 12: A compost bin that has a volume of 12 cubic feet. (2 x 2 x 3)
Therefore, there are six different sizes of compost bins the landscaper can choose from to hold exactly 12 cubic feet of compost. These sizes are 1, 2, 3, 4, 6, and 12 cubic feet.