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It is the Class of 1984’s High School Reunion. Soon, they will be celebrating together all of the high school graduates and even the alumni from previous years. A booklet is created for each high school reunion showing all of the people who passed away from all of the previous years from that high school. Each page is dedicated to a decade. Each page has the same amount of space no matter how many people died. If each page is dedicated to one ten-year span, will each page include 10 years of people who passed away? Use the factors of 84 to determine whether this will be true and explain your reasoning.
There are many factors for 84. The factors for 84 can be found by looking at all of the numbers that are 84 and fewer. Ask yourself. Does that number divide into 84 without a remainder? If so, then that number is a factor for 84. If not, then it isn’t a factor for 84. Think about it. Half of the numbers will not divide evenly except for 84. Also, keep in mind that each factor will have a factor partner. However, some factors are factor partners with themselves.
So, the factors for 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
With the booklet for the people from the high school that passed away, each page includes 10 years. However, 10 is not a factor of 84. Therefore, the last page will probably only include the last 4 years of the 84 years. Even if it doesn’t, one page will need to be only 4 pages, and the rest could be 10 years each.
A sports stadium averages about 84 people entering at any hours during the time a game is being played at the stadium. A turnstile gate was built to count the number of people entering the stadium in order to keep track of the numbers for statistical purposes. This average of 84 people shows that they fall into 6 equal categories of fans. There are the season ticket holders who primarily go to every game, the non-season ticket holders who attend every game, fans who come to about ¾ of the games, fans who come to about ½ of the games, fans who come to 1/3 of the games, and then the fans who only come to 1-2 games per season. Since there is an equal number of fans in each category, how many people on average are in each category?
There would be 14 fans per category. The best way to find this answer would be to look at the factors of 84. It would be 14 because there are 6 categories, and 6’s factor partner is 14.
Unfortunately, in a mansion there are 84 windows that need to be replaced. However, the owner can afford it since he owns a mansion. The contractor states that installing 84 windows will take about one full week to complete this project. How many windows can the contractor put in each day of the week if he puts in the same amount of windows each day?
The contractor will be able to put in 12 windows a day if he needs 7 days. This is because 7 times 14 equals 84.
It takes 84 seconds for the fastest pickle eating contest winner to consume the largest amount of pickles in the contest. At the annual Fairfield Pickle Eating Contest, each contestant is given 100 pickles to fully consume. Then each player is timed. What is the average amount of pickles the fastest pickle eater eats every quarter of the time? Use the factors of 84 to find your answer.
So, 4’s factor partner is 21. So, every 21 seconds, the eater eats 25 pickles because ¼ or a quarter of 100 is 25.
You would notice that you are missing a factor if there is a factor on your list and the factor does not have a factor partner. Remember, all factors have a partner because the factor and the factor partner multiplied together would equal that number. However, keep in mind that some factors can be to themselves to equal that number.
The factors for 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. There is a large number of factors for 84, but that doesn’t mean that all large numbers have a large number of factors. The number 82 doesn’t have very many, but this number, 84, does.
There are not a lot of things that come in groups of 84. Some objects like curtain rods and curtains are measured out to 84 inches. There would be other objects that are measured or contain 84 objects, but that would most likely be merely by chance.
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