A store manager just received 117 movies packaged in boxes. If the same number of movies are in each box, how many boxes could have been received?How many movies would be in each box?Could you Explain how you arrived your answer.

117=9*13

So it could be 9 boxes of 13 each, or 13 boxes of nine each.

or

117 = 3*39

It could also have been 3 boxes of 39 or
39 boxes of 3 each.

or even

117 boxes with 1 each or
1 box with 117 movies

3*117=351*39=689/1=689 boxes / boxes w/movies

To find the number of boxes that could have been received, we need to find a factor of 117. A factor is a number that divides evenly into another number.

To determine the factors of 117, we can start by dividing it by the smallest prime number, which is 2. However, 117 is an odd number and not divisible by 2.

Next, we move to the next prime number, which is 3. We divide 117 by 3, and it divides evenly. Therefore, 3 is a factor of 117.

Now, we divide 117 by 3 to get another factor. 117 ÷ 3 = 39.

We can continue this process until we reach a factor that is greater than the square root of 117, which is approximately 10.82. This is because if there is a factor greater than the square root, there must be a corresponding factor smaller than the square root.

Let's continue dividing:
39 ÷ 3 = 13
13 ÷ 13 = 1

So, we have the factors of 117: 1, 3, 13, 39, and 117.

Since we are looking for the number of boxes with the same number of movies, the number of movies in each box could be any of these factors. Therefore, the possible numbers of movies in each box are 1, 3, 13, 39, and 117.

To summarize:
- The possible numbers of boxes that could have been received are 1, 3, 13, 39, and 117.
- The possible numbers of movies that could be in each box are also 1, 3, 13, 39, and 117.