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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.
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.
The Chamber of Commerce building in Sunset, Alaska has 52 doors going to various rooms and closets. After much consideration, the maintenance staff has been tasked with painting the doors white with a fresh coat of paint. To do this, they have divided the number of doors with their maintenance staff members. With 6 members, will each member have an equal number of doors to paint than the other members of the maintenance staff? Why or why not?
The maintenance staff has an issue with dividing the doors to be painted with the rest of the staff members. That is because there will not be an equal number of doors for each staff member. Six cannot divide equally into 52 without having a remainder. The remaining amount of doors will need to be given to the staff members. There is not a factor partner for 6. Six goes into 52 eight times with a remainder of 4.
Brooklyn’s Stampede Bridge Club is meeting for their monthly bridge game. Four players play at a time during a game of bridge. With a deck of 52 cards, the entire deck is handed out equally to all four players. How many cards will each player get?
Using the factors of 52, you can figure out that 4 must be a factor of 52 because 4 goes into 52 evenly if each player gets an equal number of cards to the other players. Therefore, you will need to find 4’s factor partner. Its factor partner is 13, so everyone playing in the game will get 13 cards each.
France has 52 regions in it. If the regions were put into an equal number within the group, what are the possibilities of grouping those 52 regions so that each group has the same amount of regions in it?
This problem involves a matter of finding all of the factors of 52, so that you can identify the number of groups there could be. Once you find the number of groups, then you can figure out the amount of regions in each group. Fifty-two has 6 factors. They are 1, 2, 4, 13, 26, and 52. So, the possibilities are that they could have 1 group with 52 regions in it, 2 groups with 26 regions in it, 4 groups with 13 regions in it, 13 regions with 4 groups in it, 26 groups with 2 regions in it, or 52 groups with 1 region in it.
The factors for 52 are 1, 2,4, 13, 26, and 52.
The best way to do this is to divide every single number between 1 and 52 to see if it will divide equally into 52 without having a remainder. You may want to use a calculator to make sure if that is possible.
There are some groups that almost always contain 52 items in it like 52 cards in a deck or 52 weeks in a year.
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