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.

Challenging Questions

In 74 years, the marriage rate in a certain city has shown that it has increased and decreased like a roller coaster. The city council has gotten together and they want to analyze the why this has occurred. In order to do that, each person on the city council must take a set of years to analyze the events that took place that year. In order for this to be fair, how many people must there be on this city council so that everyone receives an equal number of years to analyze? Use your knowledge of factors to answer this question.

Answer

In order for the members of the city council to have the exact same number of years to analyze for this research project, the number would need to be a factor of 74 since there are 74 years. So, the factors of 74 are 1, 2, 37, and 74. That does not provide a lot of options. So, there could be just one person on the city council, but that is unlikely. Also, there could be 74 members on the city council, but that is unlikely too since most city councils don’t have that many board members. Last, there would have to be 2 or 37. Neither of those seem right since 2 is too small of a number for city council members, and 37 seems to be too many. It is unlikely that they will be able to divide up the years equally.

At a dealership, 74 cars are awaiting their inspection in the service department. The sales staff would like for those 74 cars to be grouped into 1 of 2 groups. Those groups would be those that run and operate perfectly without needing any repairs or modifications to them. The other group would be that they need some work. If there is an equal number of cars that fit into each group, explain how the factors of 74 plays a part in this.

Answer

This situation would be that the equal number of cars would have to do with the number of groups. There are 2 groups, so the equal number of cars is 2’s factor partner. This factor partner is 37.

A child is creating a macaroni art design by gluing macaroni pasta to a piece of construction paper. She glues down 74 pieces. How many different shapes could she make if she uses equal number of macaroni pieces?

Answer

In this case, the child most likely made 2 shapes with 37 pieces of macaroni. However, she could have made 37 shapes with 2 pieces of macaroni, but it is unlikely.

Frequently Asked Questions

There are 4 factors for the number 74, and they are 1, 2, 37, and 74.

An even number with factors means that 2 will always be a factor of that number. So, in this case, 2 is a factor for 74, but it also means that there is another factor for 74. The factor partner for 2 is 37 because 2 times 37 equals 74.

To find the factors of 74, write down 1 and the number itself. Then, see if it is an even number, which it is. Find 2’s factor partner which is 37. Next, see if there are any other numbers between 3 and 36 that equally divide into 74 without having a remainder. There are no more for 74.