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By 2022, there have been 46 presidents in the United States. In your social studies class, you must memorize them for an upcoming test. You want to group the presidents and memorize a group at a time. You think this will make it easier to remember them for the test.
How can you group the presidents into equally-sized groups? Is this possible? Describe whether this seems reasonable. Also, use the factors of 46 to answer these questions.
Factors of 46 are 1, 2, 23, and 46
There are not a lot of factors for 46. We automatically know that two factors would be 1 and itself, 46. However, there are two more because 46 is an even number.
So, two and its factor partner are also factors. That would be 2 and 23. Let’s check for the rest. Look at the list below. It shows the numbers between 1 and 46.
With the presidential memorization task, you now can see if you can use the factors of 46. There are only 4 factors for 46. They are 1, 2, 23, and 46. It doesn’t seem like a reasonable way to divide these 46 presidents into equally-sized groups. You could group them into 2 groups of 23 or 23 groups of 2 each, but that would not seem helpful.
It would be best to group them in unequally-sized groups. Then you could spend time studying 5-8 presidents at a time. However, the groups would not be equal in the amount.
You would notice that you are missing a factor if there is a factor in your list and there is no factor partner for that number. Also, that number could not be multiplied to itself to equal the original number like 46. For example, let’s say you have 2 in your list for 46, but you only have 1, 2 and 46. Obviously, you are missing another factor because 2 must have a partner to multiply to it to equal 46. You are missing its factor partner. This would be 23 because 2 times 23 is 46. In some cases, the factor’s partner is itself.
Someone might have trouble finding all of the factors for the number 46 because it looks like 46 would have a large number of factors. First it is an even number. Second, it looks like it might be evenly divided by 3, but it isn’t. There would be a remainder if you tried to divide 3 into 46.
All of the factors for 46 are 1, 2, 23, and 46, so there are only 4 factors for the number 46. Usually, numbers as large as 46 have more factors, so this might be a little unusual for a number like 46 to only have 4 factors.
There are not a lot of groups that normally have 46 things in them. You may see 46 minutes or other measurements. However, most don’t come in groups of 46. That is such a large number that most objects would not come in that size. The only thing that has 46 of them would be the presidents in the United States. By 2022, there have been 46 presidents since George Washington took office back in 1789. If you need to convert measurements or are working measurements, then you may happen to see something that is 46 inches, 46 feet, or 46 miles long.
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