Introduction
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.
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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
Question 1List the factors of 80
Which positive whole numbers divide 80 without leaving a remainder?
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 80
Which multiplication pairs have a product of 80?
80 has these positive factor pairs: 1 × 80; 2 × 40; 4 × 20; 5 × 16; 8 × 10.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 80
What is the prime factorization of 80?
80 = 2 × 2 × 2 × 2 × 5.
Every number in the product is prime.
