Introduction
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?
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.
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Challenge Questions
Question 1List the factors of 55
Which positive whole numbers divide 55 without leaving a remainder?
The factors of 55 are 1, 5, 11, 55.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 55
Which multiplication pairs have a product of 55?
55 has these positive factor pairs: 1 × 55; 5 × 11.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 55
What is the prime factorization of 55?
55 = 5 × 11.
Every number in the product is prime.
