Factors of 54

Introduction

With 54 independent countries in Africa, a social studies teacher provides her students with the map of those countries. She tells her students that they must color the map using different colors and then they will need to memorize these countries for a test. She recommends color-coordinating the countries by placing them into groups and then study each group at a time. Bridget wants to keep her map organized, so she decides she will organize the countries into equal groups. Help Bridget to make a plan organizing the 54 countries into groups. Explain the possibilities for Bridget.

Factors of 54

How can we break down 54 to find its factors? One way to do this is by using dollars. Let’s say that you have 54 dollars. You can group this into evenly distributed groups. That means there will be the same number of bills in each group.

So, after looking at the money groups, these represent the factors of 54. In the first group, there is 1 group of 54 dollars or you could imagine that each dollar is in a different group. You would have 54 groups of 1. In group 2, you have two groups of 27 dollars each. Again, this could represent the opposite with 27 groups of 2 dollars in each group. In the third group, you have 3 groups of 18 dollars each or 18 groups with 3 dollars in each group. Finally, the last group, 4, has 9 groups of 6 dollars in each group. You could also have 6 groups with 9 dollars in each group.

Therefore, our factors for 54 are the following:

For Bridget, she has several reasonable options for grouping the 54 countries. She would not group them into 1 big group, 54 little groups or 2 big groups or 27 small groups. That would not be reasonable for Bridget. So, Bridget can use 3 colored pencils and place 18 countries in each group. She could do the opposite in which she has 18 colored pencils and 18 groups with 3 countries in each group. She could also have 6 groups of 9 or 9 groups of 6.

Challenging Questions