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.
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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.
Challenging Questions
Question 1List the factors of 46
Which positive whole numbers divide 46 without leaving a remainder?
The factors of 46 are 1, 2, 23, 46.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 46
Which multiplication pairs have a product of 46?
46 has these positive factor pairs: 1 × 46; 2 × 23.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 46
What is the prime factorization of 46?
46 = 2 × 23.
Every number in the product is prime.
