Introduction
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.
Factors Of 82
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.
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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.
Challenging Questions
Question 1List the factors of 82
Which positive whole numbers divide 82 without leaving a remainder?
The factors of 82 are 1, 2, 41, 82.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 82
Which multiplication pairs have a product of 82?
82 has these positive factor pairs: 1 × 82; 2 × 41.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 82
What is the prime factorization of 82?
82 = 2 × 41.
Every number in the product is prime.
