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A standard NBA season schedules 82 games for each season and each team. You purchased season tickets for one at the beginning of the season for your favorite NBA team. However, your family wants you to divide the tickets among them. There are 7 members, including yourself, in your family. Use the factors of 82 to explain whether or not you can equally divide the tickets among your family members. Then, explain the best possible solution to make your family happy with the season tickets.
A factorization tree can show you the factors of 82.
With the number 82, 1 and 82 are already factors of 82 because all numbers have factors of 1 and itself. You can immediately know that 2 is a factor because 82 is an even number. Now, you need to find 2’s factor partner which is 41. Now, you need to try 3, but 82 is not a multiple of 3. Now, check 4. Nope, four isn’t a factor because when you divide 4 into 82, there is a remainder. Five is not a factor because five would also have a remainder. Try the next set of numbers. Those would be 6 through 40. If you check those, you will find out that there are no other factors.
Now, that you know the factors of 82, you may realize that the only factors of 82 are 1, 2, 41, and 82. Since there will be 82 season tickets, you need to divide it by 7. However, 7 is not a factor of 82. Therefore, you cannot divide the tickets equally among your family members. You would need a number that has a factor of 7. The closest number to 82 that has a factor of 7 would be 84. So, you would need to buy 2 more regular tickets for 2 other games. Then everyone in the family would have the same amount of season tickets and go to the same number of games.
A student is assigned to do a research project about the mountain chain in your geography class. The project consists of a research paper. Therefore, the teacher taught the students to look through at least 6 sources to find their facts. They must use at least 4 of those sources in their papers. Once the facts are collected, each fact will be written down on an index card. Then, it will be easier for the student to sort the cards into similar categories based on what they have in common. For this student, there are 82 facts to consider when writing his research report. The student has collected these 82 facts from various sources. Now, the student needs to sort the cards or facts into those groups. After looking through the cards, the student notices that he can group them into the following categories: appearance, history, tourism, people, and statistics. Will the student be able to sort the cards into equal amounts for the categories?
No, the reason there will not be an equal number of cards in each category is because there are 5 categories, and 5 is not a factor of 82.
At a children’s bake sale, the two children realized that they sold 82 candy bars to the public as the people went around to the garage sales in their neighborhood. There were 2 different kinds of candy bars. One kind is the Snickers candy bar, and the other is Kit Kat. What is the average amount of candy bars sold?
You would need to know the factors of 82 to determine the answer to this question. Since 2 is a factor of 82, we can find the average. The average amount would be 2’s factor partner. This would be 41. So, there would be an average of 41 Snicker bars and 41 Kit Kat bars.
When Albert was born, he was diagnosed with a heart disease that would need to analyzed by a cardiologist every 5 years. So, when Albert was 5, his mother made an appointment with the local cardiologist. He saw Albert and did several procedures to make sure that Albert’s heart was doing what it was supposed to do. After that, Albert continued to see the doctor every 5 years with the same procedures being done. Now, Albert is 82. Will Albert be going to the doctor this year? Use the factor of 82 to determine that.
At 82 years old, Albert would be going to the doctor considering the number of years has not changed. The reason is because 5 is not a factor of 82. Instead, the next year that Albert would be going to the doctor would be 85 because 5 is a factor of 85.
There are not many things that come in groups of 82 because 82 is such a high number. In most cases, the only things that come in groups of 82 would be randomly. That means that it just happens by chance. It could be that there are 82 people, objects or toys. Usually, things don’t come in large groups of 82 because that number is so big.
You would need to know the factors for 82 because you may have to further answer questions and work problems after you have figured out the factors for 82. Finding the factors of 82 may be the first step. Then you may have to use some or all of the factors of 82 to further work the problem.
These factors are 1, 2, 41, and 82. There are only a few factors, which is unusual since 82 is an even number. This means that 2 is factor of 82 along with its factor partner. There are no other numbers that equally divide into 82 without having a remainder.
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