# Factors of 63 ## Introduction:

Past high school data is being collected by a local city organization. The graduation years were divided among two clerks at the organization. The first clerk, Tommy, took the first 63 years, and Evelyn took the last 63 years. Each clerk had to spend time researching and gathering the data for each of those years. It is a time-consuming process. The two clerks learn that it is more time-consuming to research each year individually and then write down that information. Instead, the two decide to group their 63 years into equal groups. What are the possibilities of the groups that the two clerks can organize the years into? Use the factors of 63 to find the answer. ## How to Find the Factors of 63 The number 63 does not have as many factors as other numbers. Just like all the other numbers, there are two factors that we know exist. Those are 1 and 63 because one and the number itself automatically divide equally into that number. However, we can eliminate 2 because 63 is not an even number. Let’s look at 3. Is 3 a factor of 63? If we divide 3 into 63, it is equally divided into it without having a remainder. Let’s check for the rest. Look at the list below. It shows the numbers between 1 and 63. So, with the high school data project, there are a number of ways that the years may be grouped. Since there are 6 factors for 63, there are actually 6 ways to group. However, there are some that you would rule out. You would rule out 1 and 63 because you would not want one big group of 63 or 63 small groups. No matter how you look at it, these are the same ways and are technically not groups that could be used. So, there are four groups left, and these are 3, 7, 9, and 21. The years could be grouped into 3 groups of 21 or 21 groups of 3. They could be grouped into 7 groups of 9 or 9 groups of 7.