Factors of 50

Introduction

In the United States, there are 50 states. An organization is grouping the states into equally-sized groups. Then each group would contain the same number of states in them. The worker in the organization hasn’t quite figured out how he wants to do this. See if you can help him. Think of the number of ways that the 50 states could be grouped together. How many groups would there be? Which option would be the best? The organization probably doesn’t want a bunch of little groups, nor do they want one or a few very large groups either.

Calculating Factors for 50

There are rules to finding the factors for a number like 50. Since this is a large number and an even number, it appears that 50 will have several factors. Let’s make sure that we get them all. We can look at a set of rules to make sure that we get all of the factors.

In the diagram, it shows that first 1 and itself are factors, so that would be 1 and 50. Second, you should determine whether the number is an even or odd number. In this case, 50 is an even number. In the diagram, you can see that this means 2 will be a factor, and we need to find its factor partner. This will be 2 and 25 because two times 25 equals 50. Since it is not an odd number, we can rule out 3 being factor for 50. Now, the last step is to find if there are any other numbers between 4 and 25 because 25 is halfway through 50. There will not be a higher number than the halfway point that is a factor of a number. So, the only other number that divides equally into 50 would be 5. Five’s factor partner is 10. So, the factors for 50 are 1, 2, 5, 10, 25, and 50.

With the organization grouping the 50 states, there are several options. There are actually 6 options total. However, we can rule out a few. As stated before, the organization does not want a really large group or a bunch of small groups eithers. Let’s first list them all.

•  1 large group of 50 states in each group
•  2 groups of 25 states in each group
•  5 groups of 10 states in each group
•  10 groups of 5 states in each group
•  25 groups of 2 states in each group
•  50 groups of 1 state in each group

Now, we can rule out the first option and the last option because those are too large or too small groups. However, we can also rule out the 2 groups of 25 states in each group and the 25 groups of 2 states in each group. Those are too large or too small either. So, there are two options left. The organization could organize them into 5 groups of 10 states in each group or 10 groups of 5 states in each group.

Challenge Questions