In the axial skeleton, the head and trunk bones are located. Here, in this part of the anatomy, there is a grand total of 80 bones. These bones include the parts of the skull, rib cage, spine, and neck. An orthopedist or bone doctor must analyze each of the 80 bones to ensure that they are properly cared for in a patient. This patient is an elderly man who is having a physical done. To make sure that his bones are strong and healthy, the orthopedist must test each bone carefully. With this patient, the doctor wants to analyze each section for 15 minutes. What is the average length of time the doctor will spend on each bone analyzing it based on the average number of bones allotted to each group? Use the factors of 80 to determine the answer.

Factor Tree for 80

A way to find the factors for 80 would be to create factor trees. Do you know what a factor tree is? It is actually a diagram with branches to show the factors of a number. Think of a family tree without the family, but it contains numbers instead. Let’s look at the factor trees for 80 below.

These factor trees include all of the factors. When those two factors are multiplied together, the answer is 80. So, 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80 are all the factors of 80. However, there are two factors that are usually missing from a factor tree. These two factors are 1 and 80. The reason they are excluded may be because 1 and the number itself are always factors of any number.

So, all of the factors for 80 are 1, 2, 4, 5, 8, 10, 16 20, 40, and 80. That’s a lot of factors.

For the axial skeleton situation, we need to know the average length of the time the doctor will spend on one bone in each group. To do this, we first need to work this multi-step problem by finding the right factor. There are four groups of bones. They are neck, spine, skull, and rib cage. Four’s factor partner is 20 because 20 times 4 equals 80. So, each group has an average of 20 bones. This does not mean there are 20 bones in each group, but this is just an average. Fifteen minutes is spent examining each group of 20 bones. So, 15 divided by 20 is 0.75. Three-quarters of a minute is 45 seconds. So, each bone is analyzed for an average of 45 seconds before moving on to the next bone.

Challenging Questions

A piece of metal is being analyzed through a scientific process by a group of students in their science class. The metal is known to contain 20% of aluminum, which means that it contains 80% of other elements in this metal. Now, let’s say that the other elements in the 80% are in equal amounts. With this information given to the students, what are the possibilities about how many elements are included in the rest of the make-up of this metal? Use the factors of 80 to find this answer.

Answer

Since there are 10 factors for 80, that means there will be 10 different possibilities about how many elements are included in the rest of the make-up of the metal. It could be 1 element that takes 80% of the metal, 2 elements with 40% each or 4 elements making up 20% of the metal. However, it could also be 5 elements of 16% each, 8 elements of 10% each, 16 elements of 5% each, 20 elements of 4% each, 40 elements of 2% each or 80 elements of 1% each.

Sleeping Beauty slept for 80 hours straight. Every 4 hours, someone would check on Sleeping Beauty to make sure she is okay. How many times did someone check on her? Use the factors of 80 to find the answer.

Answer

A person would have checked on Sleeping Beauty 20 times if they checked every 4 hours since Sleeping Beauty slept for 80 hours straight. The reason is because 20 times 4 equals 80. Remember, 4 and 20 are factors of 80.

Eighty cups of water are set out during a marathon on a table near the area where the marathon runners will pass by. They have set up a long couple of rows in order to make it easier for the runners to swipe up a cup of water without having to stop. The person who set up these cups of water did not want to make many rows on the table. This would mean that runners would have to reach further across the table to grab a cup of water or they would have to stop. So, how many cups of water will be in a row if there are only two rows of cups of water?

Answer

Since there are 80 cups of water in 2 rows, then there would be 40 cups per row because 40 times 2 equals 80.

Frequently Asked Questions

To find the factors of 80, you will need to know that 1 and 80 are automatically factors of 80 because all numbers have factors of 1 and itself. Then, you may notice that 80 is an even number. So, 2 is a factor for 80. Two goes into 80 forty times. So, 2 and 40 are factors of 80. The next steps would be to see if the next numbers from 3 to 39 can divide into 80 without having a remainder. In this case, there are some of those numbers that can divide evenly into them and some cannot. The numbers 4, 5, 8, 10, 16, and 20 are also factors of 80.

If you have to factor, you most likely have to divide with word problems. You can always use factoring when you are trying to find a number that equally divides into a number without having a remainder. Then there may be another step to this word problems for you to calculate.

You need to find all of the factors of 80 to make sure that you have the correct answer especially when you are grouping objects.