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Heinz 57 makes ketchup. Their number 57 actually comes from other products that they make. It actually means that they have 57 varieties of pickles, believe it or not. So, at the Heinz factory there is a group of employees who are responsible for a set of the pickles. Use the factors to figure out how many employees there could be in the group and how many different types of pickles each employee in the group is responsible for. See if you can figure out both numbers based on the factors of 57.
Factors of 57 are 1, 3, 19, and 57.
There are certain steps with finding the factors of a number like 57.You may be able to tell right off the bat that 57 does not have a lot of factors for it. First, it is not an even number. Second, it is not a number that has a single-digit multiplication fact for it. However, let’s dig in and see if we can find all of the factors. There might be a surprise set of factors in there that you might not have thought of.
With the Heinz 57 problem, the group of employees could be either 3 or 19 employees. If there are 3 employees, then each of those employees would be responsible for 19 varieties of pickles. On the other hand, there could be 19 employees in the group, and each of the employees in this group would be responsible for 3 varieties of pickles.
A car lot has 57 vehicles for sale. It just so happens that he has an equal amount of each of the following types of vehicles. He has motorcycles, sedans, pick-up trucks, and SUVs. Determine if this is possible for the car lot to have 57 vehicles total and an equal amount of vehicles with these types.
There is no way that the car lot could have 4 types of vehicles: motorcycles, sedans, pick-up trucks, and SUVs with the 57 vehicles equally dispersed in those categories. The reason has to do with the factors of 57. There are certain factors for a number such as 57. These numbers include 1, 3, 19, and 57. So, 4, which is the number of vehicle types, is not a factor. Therefore, some groups would have more in them. The car lot either didn’t have 57 vehicles or there were other types of vehicles than those listed.
In a general meeting, there are 57 seats arranged for the members of the board and audience. Think about how they could be arranged so that there is an equal amount of chairs for both the 3-member board and the rest of the rows?
Since the member board consists of 3 people, then we need to start with that. Each row must contain 3 seats in it in order to be consistent with the number of chairs for the board. Now, we can find 3’s factor partner. That would be 19. So, there would be one row at the front of three seats for the member board. Then, there will be 18 rows of three seats in each row for the audience.
There are 57 sentences for the editor to edit. If he edits 19 lines in 2 minutes, how long will it take him to finish editing? See if you can use the factors of 57 to find your answer.
Since 19 is a factor for 57, then we need to find 19’s factor partner. This would be the number that can be multiplied to 19 to equal 57. This would be 3. So, then we need to multiply 3 with 2 because there are 3 groups of editing based on the 19 lines each. This would be 6 minutes. So, the editor can edit 57 sentences in just 6 minutes.
The reason that someone might have more trouble finding the factors of 57 is because first there are not a lot of factors for 57. Also, it does not appear that there are more factors than 1 and itself. Many people might forget that 3 and 19 are factors of 57 because it just seems that 57 doesn’t have any more factors than 1 and itself.
There are not a lot of items that come in groups of 57. Usually, objects do not come in such large groups anyway, but even less seem to come in groups of 57. The only thing would most likely be Heinz 57. That is not necessarily a group of something though. It is just that 57 is associated with Heinz 57 often.
To make sure that you have the complete set of factors for 57, you will need to divide each and every number from 1 to 57 into 57 and make sure that there is not a remainder for any of those numbers after dividing them into 57. If there are, then the number is not a factor of 57. One way to keep track of this would be to use a chart.
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