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In a 55-gallon drum, it needs to be filled with different kinds of rocks in order to create a heavy weight to keep doors open and tarps down on the ground from blowing away. Since the gallon-drum owner is frugal, he goes straight to the clearance aisle of the rock store. Since it is a clearance aisle, there are only a few gallons worth of each type of rock. So, the owner decides to get an equal amount of rocks to place into the 55-gallon drum. How could the owner best do that using the factors of 55?
Look at the images below. They show two groups of objects. These have to do with the factors of 55.
This image shows 5 groups. Each group contains 11 colored pencils in it. This represents the factors. The number 55 has two factors of 5 and 11. We could regroup these into 11 groups of 5 colored pencils each.
This shows how the 55 objects or rubber ducks can be grouped into 11 groups of 5 each. So, we have four factors for 55. You always have two factors no matter the number. Those two numbers are 1 and itself. So, 55 has factors of 1 and 55. It also has 5 and 11 as shown in the images.
Back to the 55-gallon drum, you now can help the owner figure out his problem. There are only a few choices since there are only a few factors that can be used. He can’t use 1 type even though 1 is a factor of 55 because there would not be enough rock from one type. Also, it is unlikely that he would purchase 55 different types of rocks. The last two factors of 5 and 11 are the most realistic choices. So, the owner could place 5 different kinds of rocks and get 11 gallon-amounts of each or 11 different kinds of rocks with 5 gallon-amounts of each.
To find the factors of 55, start with one and itself, 55. Then know that you can skip 2 because 55 is not an even number because it is an odd number. Next, divide 55 by 3. It is not a factor for 55 because there would be a remainder. The same will happen with 4. If you divide 4 into 55, there would be a remainder of 3. Next, you will have to see if 5 through 54 are factors of 55 by dividing them into 55 to see if there is a remainder. For the number 5, there is not a remainder. Eleven is also a factor for 55 because it will equally divide into 55. As a matter of fact, 5 and 11 are factor partners because when you multiply 5 and 11 together, it will equal 55. The other numbers are not factors of 55 because there would be a remainder.
There are only a few instances when you will use the factors for 55. There are 55 mile-per-hour speed limits, 55-inch television sets, and 55 and over communities. There are other groups of 55, but they would be random objects that just happen to have 55 objects in them.
There are 4 factors for 55. They are 1, 5, 11, and 55. Since it is an odd number, there are usually fewer factors than a number that is an even number, but not always.
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