## Introduction

At a large hardware store, it sells many different types of bathroom parts including shower stalls, toilets, and bathroom vanities. As you search for the right one, you realize that you will need to know the measurements of the place in your bathroom for the bathroom vanity. You can’t just place any bathroom vanity in that spot. So, you know that the area of the bathroom is 36 inches squared in area. What possibilities could there be based on the area?

Even though you still can’t pick any of the ones that are possibilities because it still must fit, you can at least narrow it down to these. See if you can use the factors of 36 to determine these possibilities.

## Factors of 36

The factors of a number like 36 are the numbers from one to the number, 36, that can evenly divide into it without having a remainder. Let’s look at a few. Of course, 1 and itself are factors. Two will be a factor too because 36 is an even number. Now, we need to find 2’s partner. It would be 18 because 2 times 18 equals 36. Below shows the other numbers from 1-36 that are factors of 36 because they evenly divide into 36 without having a remainder.

With 36, there are quite a few factors. These factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. This means that your bathroom vanity could be 2 inches by 18 inches, 3 inches by 12 inches, 4 inches by 9 inches or 6 inches by 6 inches. However, some of those possibilities seem a little too thin. Most likely, the possibilities that seem reasonable would be the vanities that measure 4 by 9 or 6 by 6.

## Challenging Questions

A dessert recipe calls for 36 grams of flour which equals to a ¼ cup. In the recipe, it states that the flour must be stirred in slowly in groups. You want to make sure that even though this is a little amount of flour, you will want to make sure that you stir the flour in equal amounts of flour. How many different choices of groups could you have?

As a student in high school, you are counting down the days until the last day of school. There are 36 days left until the end of the school year. Unfortunately, this means that there are 36 days left until this student’s end of course exams. He has 6 courses to study for. Use the factors of 36 to figure out how many equal number of days this high school student can allot to each course if he only want to study one course a day.

At the local ice cream shop, Patty is in charge of arranging the 36 ice cream toppings so that the customers will be able to see them. What possibilities does she have? Use the factors to figure this out.

When you factor numbers, you are finding the numbers that can evenly or equally divide into that number without having a remainder. For example, 4 is a factor of 36. When you divide 4 into 36, it goes nine times. There is no remainder. However, if you divide 5 into 36, there would be a remainder. Five goes into 36 seven times. However, 5 times 7 is 35. There would be a remainder of 1. Then 5 would not be a factor of 36.

This can mean one of two things. It can mean to find the factors of 36 which means to find the numbers that can evenly divide into 36 without having a remainder. However, there is another math skill that has to do with factoring. This type of factoring has to be with division too. It can also relate to multiplying.

To be sure that you have all of the factors for a number like 36, you need to actually check each and every number between 1 and 36. You can use a calculator. Take the calculator and see if you divide numbers 2-35 into 36. If there is a remainder, then that number is not a factor for 36. Then match each number with its factor partner. These partners multiplied together should equal 36. It is always good to check and double check to make sure that you have all of the factors. The number 36 has several factors.

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