# Factors of 74 ## Introduction

You walk into a ballroom for couples’ ballroom dancing. You have invited 74 people to attend this ballroom dancing group. In order for this to be successful, you make sure that you have an equal number of men to women in this group. That way, everyone will be able to participate in the ballroom dancing practice at the same time. People will not have to share partners. As you walk in, you need to space each couple apart in order for them to have enough room. How many spots will you need to designate on the floor based on the number of couples? Use your knowledge of the factors of 74 to find your answer.  ## 74 Factors

There are only four factors for 74. Let’s figure out how to find them. First, there is always one group of 74 and 74 groups of 1. This means that 1 and 74 are factors of 74. As a matter of fact, one and the number itself are always factors of that number.

Look at the images below. They show two groups of objects. Each group has to do with the factors of 74. In this first image, it shows two handfuls of candy. Each handful has the exact amount as the other handful. So, they are the same. Each handful has 37 pieces of candy in it. If we divided 37 into 74, we would get an equal number without a remainder. That number would be 2 because 2 times 37 equals 74. Both 2 and 37 are factors of 74. This is because 2 and 37 are factor partners.

Now, look at this next image. This shows that there are 37 groups of 2. There are 2 pieces of chocolate, and there are 37 groups. This shows the factors also of 74 with 2 and 37. Back to the ballroom dancing, you now can help figure out this problem. It can only be one answer. You know that there are 74 people with an equal number of men to women. This was set up on purpose, so that every couple could dance and practice at the same time. A couple means that there are 2 people in the group. So, we need to find 2’s factor partner. We have learned that the factor partner for 2 is 37 based on the groups of candy above. So, there needs to be 37 spots allocated on the floor that are distanced enough apart for the ballroom dancers to have enough room to dance. Hopefully, the ballroom is large enough to accommodate this.