Factors of 84

Posted on31 May 2022

Introduction

It is the Class of 1984’s High School Reunion. Soon, they will be celebrating together all of the high school graduates and even the alumni from previous years. A booklet is created for each high school reunion showing all of the people who passed away from all of the previous years from that high school. Each page is dedicated to a decade. Each page has the same amount of space no matter how many people died. If each page is dedicated to one ten-year span, will each page include 10 years of people who passed away? Use the factors of 84 to determine whether this will be true and explain your reasoning.

The Many Factors of 84

There are many factors for 84. The factors for 84 can be found by looking at all of the numbers that are 84 and fewer. Ask yourself. Does that number divide into 84 without a remainder? If so, then that number is a factor for 84. If not, then it isn’t a factor for 84. Think about it. Half of the numbers will not divide evenly except for 84. Also, keep in mind that each factor will have a factor partner. However, some factors are factor partners with themselves.

So, the factors for 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

With the booklet for the people from the high school that passed away, each page includes 10 years. However, 10 is not a factor of 84. Therefore, the last page will probably only include the last 4 years of the 84 years. Even if it doesn’t, one page will need to be only 4 pages, and the rest could be 10 years each.