# Factors of 52

## Introduction

At a large corporation with thousands of employees, the company had to make arrangements with its employees who work around the world. There are 13 branches located in 4 different hemispheres around the world.

They had to make sure that they did not have too many employees taking their week-long vacation break all at the same time.

Unfortunately, last year, that was an issue when the vacation rule was unlimited as to the time when any employee around the world could take their vacation. About 1/3 of the employees chose to take their vacation during the same week.

That caused production to decrease dramatically. This led to customers having to receive their products extremely late, and many of the product orders were cancelled as a result. Needless to say, the quarterly reports for that time were not very good.

So, the administration had to make a change. They want to group their employees from each branch and provide them with a separate set of weeks. Use the factors of 52 to determine how many weeks each branch can choose from for their vacation week.

## Using A Factor Tree for 52

One way to find the factors for 52 would be to create a factor tree. This diagram is one way to figure out all of the factors of a number by breaking down the number. You will need to keep up with the factors as you break down the number.

Let’s look at 52’s factor tree. See if you can first figure out the factors of this number by analyzing this diagram.

This factor tree shows all of the factors for 52. It is good to know that there are two other factors that have not been shown on this tree. Those are 1 and 52.

However, normally you would not bring the first 2 down, but it is needed to show all factors for the number, 52. So, on the first line, 2 and 26 are factors of 52. On the last line, factors come in pairs. So, we need to multiply some numbers together to get the two other factors.

If we multiply 13 and 2 together, we get 26, which is already a factor for 52. Therefore, we need to multiply the 2 and 2 together which would be 4. So, 4 and 13 are factors for 51.

Since 13 is a prime number, I can’t break it down any further. The same is with 2. So, I know I am finished with my factors.

## The factors for 52 are 1, 2, 4, 13, 26, and 52.

With the large corporation that was dividing up their weeks of the year, the corporation can equally divide the year and provide each of the 13 branches of the company with the same number of vacation weeks. The factors of 52 are 13 and 4.

These are both factors for 52, and they are factor partners. So, each of the 13 branches of the corporation will have 4 weeks at some point in the year for their employees to choose from and take their vacation.