At a popular company, a job advertisement for a receptionist was placed on an online job board website. Forty-two applicants applied for this position. The human resources department runs the applications through a computerized process that sorts them into groups.

These groups are above average, average, and below average. The human resources department will then discard the below average applications based on their skills.

The other two groups will be analyzed by the department before interviews are decided.

Could there be an equal number of applications in each group?

To do this, you will need to know the factors of 42. This will then let you know whether there was an equal number of applications in each group.

Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42

The factors of 42 can be determined by seeing what numbers can divide into 42 without having a remainder. In the factorization tree below, it shows the factors of 42. The tree will show the numbers that can divide into 42 without a remainder and it also will show its factor partner.

This is one factorization. It shows that 2 and 21 are factors of 42. We can also figure out that 3 times 2 equals 6, so 6 and 7 are factors as well. We could also use this factorization tree by multiplying 7 times 2. This would be 14, so 3 and 14 are factors of 42.

Therefore, the factors are 1, 2, 3, 6, 7, 14, 21, and 42.

With the job that had 42 applicants apply for it, they were separated into three groups: above average, average, and below average. So, there were three groups. The factor that could be multiplied to 3 in order to equal 42 is 14. So, there are 14 applications in each group.

Challenging Questions

At the Harper Tire Company, there are 42 employees total. However, not all of the employees work at the same building. This is because Harper Tire Company has 3 locations. How many employees would be at each location is there are the same number of positions at each location?

Answer

There would need to be 14 employees at each location. This can be figured out by using the factors of 42. The number 3’s factor partner is 14, so 14 times 3 is 42, or 42 divided by 3 is 14.

After two semesters, you look at all of the assignments in your history class. There were 42 assignments. Each assignment was placed in a category. However, there happens to be an equal number of assignments in each category because your history teacher likes consistency. So, there were an even number of tests, projects, essays, etc. You count the number of tests, and there were 7 tests. How many categories would there be if you used the factors of 42 to find your answer?

Answer

There would be a total of 6 categories. You already know that there were 7 tests. Based on the information, the teacher gave the same number of each type of assignment. That means there were 7 projects, 7 essays, etc. So, 7’s factor partner would be 6, so there are 6 categories with 7 assignments in each for a grand total of 42.

Unfortunately, obesity has been on the rise. Statistics show that obesity is up 42% since 50 years ago. If for a project, you want to know the average percentage rise in obesity per decade, would there be a whole percentage number or would it be a fraction? Use the factors of 42 to figure it out.

Answer

There would be a fraction. First, there are 10 years in a decade, so 10 divided into 50 would be 5. Five is not a factor of 42. Instead, there would be a remainder of 2. This would determine that a fraction would be a part of the number.

Frequently Asked Questions

To find the factors of 42, you will need to know that 1 and 42 are automatically factors of 42 because all numbers have factors of 1 and itself. Then, you may notice that 42 is an even number. So, 2 is a factor for 42. Two goes into 42 twenty-one times. So, 2 and 21 are factors of 42. The next steps would be to see if the next numbers from 3 to 20 can divide into 42 without having a remainder. In this case, there are some of those numbers that can divide evenly into them and some cannot. Three and 14 are factors because they don’t have a remainder. Six and seven also are factors of 42. They don’t have remainders either.

With word problems, if you have to factor you will most likely have to divide. Depending on how difficult the problem is, this will depend on how many steps you will have to take. You can always use factoring when you are trying to find a number that evenly divides into a number without having a remainder. Then there may be another step to this word problem for you to calculate.

You might need to find the factors for 42 if a word problem needs you to find a number that can divide into 42 without having a remainder. There are some instances when things would come in groups of 42. This is a large number, so there may not be as many as there would be with smaller numbers. It is also not a round number like 50 or 45. However, there are some things that come in 42 inches like a bathroom vanity or 42 degrees with temperature. Otherwise, some things would only come in groups of 42 by chance. There may be 42 nails in a box or 42 employees at a company. These would not be typical circumstances.