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In a kindergarten class, the teacher wants to teach her students the letters of the alphabet. Of course, there are 26 letters in the alphabet. The teacher wants to group the letters based on what they have in common instead of teaching each one separately.
She also wants to spend an equal number of time on each letter, so her groups she have the same amount in them as the other groups. If you were the teacher, what would be the best way to teach the letters to a group of kindergartners who are just starting out learning about the alphabet and the letters’ sounds.
To find out how to do this, the best way is to use factoring.
Factors of 26 are 1, 2, 13 and 26
Factoring is an easy task. However, keep in mind that there is no way to immediately know how many factors belong to a number. You have to go through the process. So, what is the process? It’s easy. You need to divide each number between 1 and 26 into 26 to see if the number will not have a remainder. If it has a remainder, then it is not a factor of 26.
Each number has at least 2 factors. These numbers are 1 and itself. So, 1 and 26 are factors of 26. However, there maybe more. We will calculate by dividing each number from 2 to 25 to see if they can be divided into 26 without having a remainder.
Look below at the list. I took each number and divided it into 26. If there is a remainder, then it is not a factor. I have listed the remainder, if there is one, and whether it is a factor or not.
You may see that there is a pattern near the end of the list. As the numbers ascend, the remainder decreases by one until the last number, 26, has no remainder. Let’s look at the factors of 26 based on the list above.
With the kindergarten teacher and her grouping of the letters, we can rule out one and 26. She can’t group the letters in those amounts of groups. So, we have two factors left, 2 and 13. We could have 2 groups of 13 letters or 13 groups of 2 letters.
Either answer would be correct, but we need to use logic to determine which one is the better answer for kindergartners. In this case, it would be best to have 13 groups of 2 letters. Having a kindergartner to learn 13 letters at a time seems difficult.
The Taylor family with their 11 children is moving to another state. They rent a 26-foot-long truck to transport all of their stuff from their current location to their new home. With 13 people in their family, they have divided up the truck so that each person has an equal amount of space. Use your knowledge of factoring to determine how much room each person in the family will get.
There are 26 feet in the truck, and there are 13 people. With 26, there are 4 factors (1, 2, 13, and 26). We need to find the factor partner for 13. Then this will show how much space each person has in the truck. Thirteen’s factor partner is 2, so each person will have 2 feet squared of space. That is not a lot of room at all, so I hope the family does not have a whole lot of stuff.
A new school system is planning out their schools. They have already determined that they will need 26 schools based on the student population in their city and the number of students allowed in each school building based on the fire code. However, they need to determine whether they can have an equal number of elementary, middle, and high schools. They would prefer to match each area of the city to have its own elementary, middle, and high school. Will they be able to do that? Use the information about factoring to explain your answer.
Unfortunately, they can’t. Instead, they will have an unequal number of school buildings when grouped into 3s. Three is not a factor of 26, so there would be a remainder of 2. This means that there would be either an elementary and middle school, middle and high school, or elementary and high school, but there would not have the third type of school.
A test has 26 questions on it. There is an equal number of questions per page. What are the combinations of number of pages and number of questions on each page?
There are four combinations. There could be one page with all 26 questions on it, or there could be 26 pages with 1 question on each page. That would be unusual. Most likely, there would be 2 pages with 13 questions on each page. Another option would be to have 13 pages with 2 questions on each page.
You will need to divide each number from 1 to 26 into 26 to see if you get a remainder. If there is no remainder for that number, it is a factor.
There are 4 factors for the number 26.
Each factor of a number comes in a set. That means each factor has a partner. In this case, 26 has 2 groups or sets of factors.
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