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As you and your family are driving down the road, you notice a sign that reads “38 miles to the next town.” That seems okay because you have some gas in your car. Think about if your car will make it to the next town for gas if you know that each gallon of gas will let you go 17 miles. Right now, how much gas must you have in order to make it to the next town.
Use the factors of 38 to determine whether you will be driving to the next town or pushing your car to the next gas station.
To find the factors of 38, we will group people. Each group of people should equal to 38 if multiplied together. If the number is not there, this means that the number cannot be evenly divided into 38. Otherwise, there would be a remainder.
With the situation with you and your family driving 38 miles to the next town, you know that each gall of gas in your vehicle will allow you to travel 17 miles. Using the factors of 38, you would need to know 17’s factor partner. In this case, the answer is 2. Two gallons is the amount needed to allow you and your family to get to the next town.
With a 38-inch guitar, you would like to create a box to fit the guitar. With the wood, you need to sand it in sections. Each section, you decide, will be 19 inches.
How many sections will you have?
You will have 2 inches because when you use the factors of 38, you will see that 19’s factor partner is 2. This means that 2 times 19 equals 38.
A dress is 38 inches long from the waist to the end of it. On this fabric, for every 2 inches there is an adjoining pattern.
Based on this information, how many patterned shapes are there?
There would be 19 shapes from the top to the bottom because 19 times 2 is 38. You would need to find 2’s factor partner. Nineteen is 2’s factor partner.
While designing a 38-foot sailboat, you decide you would like to paint a large stripe across the 38 feet from one end completely to the other end. If you want to change the color by using the ombre pattern, think about how you would go about doing this. Ombre is a change of color subtly from one color to another. You want to include 7 colors. Explain how you could do this equally, so that each color only covers the same amount of space as the other colors.
Could this occur? Explain your answer using the factors of 38.
In this case, you could not do that. The main reason is because 7 is not a factor of 38. When you divide 7 into 38, you would have a remainder. That means one color would be longer than the other colors. There is really no way you could do this because you can’t add any feet onto your boat. You would actually need to have 19 colors in order for all of the colors to be equally in size to each other.
The rules of finding the factors of 38 begins with 1 and the number itself. So, the first numbers for 38 are 1 and 38. Since 38 is an even number, 2 is a factor of 38. Then find its factor partner. That would be 19 because 2 times 19 equals 38. Then, you need to see if 3 can evenly divide into 38 without having a remainder. In this case, there would be a remainder. So, 3 would not be a factor for 38. We only have to look at the numbers between 3 and 16. Four is not a factor either because it would produce a remainder. Five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, and sixteen are not factors of 38. These would all have remainders. So, the number 38 does not have a lot of factors. It only has 4 of them. These are 1, 2, 19, and 38. However some people may have trouble with factoring 38. They may think that there are more factors because it is an even number and it is a larger number. Usually, larger numbers have more factors because more smaller numbers can evenly divide into them. However, that is not true for number 38.
Factoring and prime factorization are different, but they do have some similarities. Factoring has to do with finding the numbers for a number that can evenly divide into that number without having a remainder. Prime factorization has to do with breaking down the factors into smaller numbers. Let’s look at an example. For 38, the factors for 1, 2, 19, and 38. These numbers can equally divide into 38 without having a remainder. For prime factorization, we would take 38 and divide it down to 2 and 19. Then we would see if those two factors can be divided down further. Can 2 be divided to a smaller number? No, two can’t be divided further down. Nineteen can’t be further divided down. There is not a smaller number below 19 that can evenly divide into 19 without having a remainder.
This question wants to know if there are objects or things that are typically grouped into 38 things. The answer is really a no because most things do not come in groups that high in number. Instead, objects are usually grouped into smaller numbered things. However, there can always be a class or group of toys or candies that have 38 in them. Yet, this would be random things.
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