Introduction
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.
Chalenge Questions
Question 1List the factors of 26
Which positive whole numbers divide 26 without leaving a remainder?
The factors of 26 are 1, 2, 13, 26.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 26
Which multiplication pairs have a product of 26?
26 has these positive factor pairs: 1 × 26; 2 × 13.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 26
What is the prime factorization of 26?
26 = 2 × 13.
Every number in the product is prime.
