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In the United States, there are 50 states. An organization is grouping the states into equally-sized groups. Then each group would contain the same number of states in them. The worker in the organization hasn’t quite figured out how he wants to do this. See if you can help him. Think of the number of ways that the 50 states could be grouped together. How many groups would there be? Which option would be the best? The organization probably doesn’t want a bunch of little groups, nor do they want one or a few very large groups either.
There are rules to finding the factors for a number like 50. Since this is a large number and an even number, it appears that 50 will have several factors. Let’s make sure that we get them all. We can look at a set of rules to make sure that we get all of the factors.
In the diagram, it shows that first 1 and itself are factors, so that would be 1 and 50. Second, you should determine whether the number is an even or odd number. In this case, 50 is an even number. In the diagram, you can see that this means 2 will be a factor, and we need to find its factor partner. This will be 2 and 25 because two times 25 equals 50. Since it is not an odd number, we can rule out 3 being factor for 50. Now, the last step is to find if there are any other numbers between 4 and 25 because 25 is halfway through 50. There will not be a higher number than the halfway point that is a factor of a number. So, the only other number that divides equally into 50 would be 5. Five’s factor partner is 10. So, the factors for 50 are 1, 2, 5, 10, 25, and 50.
With the organization grouping the 50 states, there are several options. There are actually 6 options total. However, we can rule out a few. As stated before, the organization does not want a really large group or a bunch of small groups eithers. Let’s first list them all.
Now, we can rule out the first option and the last option because those are too large or too small groups. However, we can also rule out the 2 groups of 25 states in each group and the 25 groups of 2 states in each group. Those are too large or too small either. So, there are two options left. The organization could organize them into 5 groups of 10 states in each group or 10 groups of 5 states in each group.
Hooray! It is Debra’s 50th birthday on Friday. Her friends and family would like to create a timeline movie of Debra’s life. Her 5 friends want to divide her first 50 years of life equally among them. Each person will take this amount of time and find pictures and events in Debra’s life to create into a movie sequence. Then all of the parts will be edited together and presented to Debra at her birthday on Friday. How many years will each friend have to cover? Use the factors of 50 to find your answer.
To find the answer, you may use the factors of 50. There are 50 years, and there are 5 friends. You need to find 5’s factor partner to find the number of years each friend will cover. The factor partner will be the number multiplied with 5 to equal 50. This would be 10. So, each person will cover 10 years of Debra’s life.
In 1950, the Department of Highway Consideration has been required to do a study to find out how many highways and roads were in consideration of being built but were not starting in 1900. Within those 50 years, every two years will be analyzed to place in a graph or chart. How many bars will be on their chart? Use the factors of 50 to find your answer.
There are 50 years that the department has to analyze, but they are grouping those years by 2 years. They most likely did not want a bar graph with 50 bars in it as that might make it difficult to read and understand. So, there would be 25 bars because 2’s factor partner is 25.
The Top 50 Songs were categorized into the following musical genres:
Now, what would be the average amount of songs in each category?
There would be 5 songs in each category. Multiply 5 times the 10 genres to equal 50.
You can find the factors of 50 by dividing the numbers from 1 through 50 into 50. If you have a remainder, then this number is not a factor of 50. If you don’t have a remainder, then it is a factor of 50.
There are a few objects that are often grouped into groups of 50. There are 50 states, a top 50 of something, as well as 50 cents.
A number is not a factor when there is a remainder after dividing the number into 50.
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