Introduction
You just turned 18 years old, and you feel it is time to write a book about your life. Think about how you could divide your life into chapters. How many chapters will you have?
You may first want to begin by thinking of the sections of your life. It could be birth, childhood, family, academics, relationships, and the future. With these topics, you want to evenly divide these topics over the 18 chapters of your book.
Can you think about how many years will be allocated for each of the 6 chapters?
To find this out, you may want to look at the factors for 18. So, what are the factors, and what are the factors of 18?
Using a Factor Tree for 18
One way to find the factors for 18 would be to create a factor tree. What is a factor tree, you ask? Actually, it is a diagram with branches to figure out the factors of 18. Think of a family tree without the family, but it contains numbers instead.
Let’s look at the factor tree for 18 below.
These factor trees include the two sets of factors that when multiplied together result in 18. So, 2, 3, 6, and 9 are factors of 18. However, there are two factors that are usually missing from a factor tree. These two factors are 1 and 18.
The reason they are excluded maybe because 1 and the number itself are always factors of any number.
So, all of the factors for 18 are 1, 2, 3, 6, 9, and 18. That is quite a lot of factors.
For the 18-year old’s book, we know that there will be 6 chapters. If there would be the same amount of years for each chapter, then each chapter would have 3 years of your life dedicated to each chapter. You could find this out based on the factor tree. As you can see, the factor tree that has a factor of 6 in it has a partner of 3.
Factors of 18 are 1, 2, 3, 6, 9, and 18
Challenging Problems
Question 1List the factors of 18
Which positive whole numbers divide 18 without leaving a remainder?
The factors of 18 are 1, 2, 3, 6, 9, 18.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 18
Which multiplication pairs have a product of 18?
18 has these positive factor pairs: 1 × 18; 2 × 9; 3 × 6.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 18
What is the prime factorization of 18?
18 = 2 × 3 × 3.
Every number in the product is prime.
Question 4Classify 18
Is 18 prime or composite?
18 is composite.
It has more than two positive factors: 1, 2, 3, 6, 9, 18.
