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A package delivery driver sees that he has 14 packages left to deliver. He wants to group them into the northern, southern, eastern, and western areas of town. Then he would drive to each area and deliver each group.
In this case, do you think he could have an equal number of packages in each group, or will there have to be different amounts of packages in each group?
The answer is no. The driver will not have an equal number in each group for each area of town. There are 4 areas of town.
Since there are 14 packages left to deliver, there may be some groups that are the same, but it couldn’t be all 4 groups. Fourteen can’t be divided equally by 4 because there would be a remainder.
Look at the groups of packages below.
The closest would be that there are three groups with four packages in each of those three groups. The last group would only have 2 packages in that group.
There are many other combinations for dividing the 14 packages into 4 groups, but it could never be with an equal number of packages in each group.
Why can’t the delivery driver have equal groups of packages? That all has to do with the factors of 14. To have equal groups of something means the number that represents the total amount must have a factor that is the same as the number of groups.
In this case, that is not true. Let’s find out the factors for fourteen. To find out, we will see which numbers 14 or fewer can equally divide into 14. There could be no remainder, or it will not be considered a factor of 14. Let’s gather the factors!
There are not a lot of factors for 14. Actually, there are four factors. One times 14 equals 14, and 2 times 7 equals 14.
Factors of 14 are 1, 2, ,7 and 14
Your mother tells you to clean your room. You have 14 minutes left do this chore since it is 2:46, and your friend will be at your house at 3 p.m. to pick you up. You must race to get this done. Your mom will not let you leave unless your room is spotless, and unfortunately, she is very picky. So, you have a great idea. You are going to divide your room in half and focus on one half of your room and then the other half. How many minutes do you have to clean each half?
You will have 7 minutes for each half of your room. The total minutes is 14. If you have half of something, then you need to divide by 2. So, here, you would divide 14 by 2 to get 7. You have 7 minutes to clean one side of your room and 7 minutes to clean the other side.
There are fourteen crayons in the package. However, this is a special package of crayons because these crayons smell good. When you color with them, they release a great scent. Unfortunately, some of the scents have died and no longer smell. Seven of those crayons no longer smell. You want to group the crayons into those that smell and those that no longer smell. Explain how you could prove with the factors of 14 the number of groups you would have.
With fourteen crayons in the package and dividing them into groups of 7 means that you would have two groups. There are four factors for 14. These are 1, 2, 7, and 14. So, 2 and 7 are partners with the factors. It means that 2 times 7 equals 14. If there are groups of 7, then there must be 2 groups due to these factors being partners.
Tiffany bought 14 candles to put into her house. She has a house with many rooms. She has 14 rooms to be exact. She wants to use all of the candles, but she wants to put an equal number of candles in her rooms. She doesn’t care whether or not she has candles in all of the rooms as long as there is an equal number of candles in the rooms that she puts candles in them. What options does she have?
She has 4 options. We would need to use the factors for 14 to find out how many options she has. Since there are four factors for 14, which are 1, 2, 7, and 14, then there are four options. So, Tiffany could put all 14 candles in one room, 1 candle in 14 rooms, 2 candles in 7 rooms, or 7 candles in 2 rooms.
There are 4 factors for the number 14. These include 1, 2, 7, and 14.
To find the factors of 14, you will need to find the numbers between 1 and 14 that can equally divide into 14 without having a remainder.
In many cases with factors, you can use factors to find out how many groups you can make with a number like 14. You may want to find out how many equal groups you can make with 14 objects. If you know the factors of 14, then you instantly know the number of equal groups you could make. Since there are 4 factors (1, 2, 7, and 14), then you have four equal groups.
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