A potential job candidate is creating his resume. He is actually going to lie on his resume. Even though he has never worked a job, he wants to show that he has worked some jobs. So, he makes some up. He decides that he should have been working for the past 34 months since he graduated from high school about that many months ago. He wants to evenly divide the months into groups and then assign each group of months to a job. How many possibilities does he have?

This is obviously not a great idea, and it is not recommended. However, since this man insists on doing this, he needs to be able to factor 34 into its factors and factor partners. Then he will know which number of jobs will seem appropriate. He doesn’t want a bunch of jobs that didn’t last long. He also doesn’t want just one job.

Factors of 34

To find the factors of 34, you need to follow a set of rules. This will ensure that you have every single factor.

Rule 1: First, the numbers 1 and the number itself, 34 are automatically factors.

Rule 2: Second, since 34 is an even number, you know that 2 is a factor. Now, we need to find 2’s factor partner. This means we need to find the number that can be multiplied with 2 to get 34. This would be 17.

Rule 3: Now, we need to see what other numbers can equally divide into 34 without having a remainder. We only need to check 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 because we know there will not be numbers above 17. These numbers will not equally divide into 34. So, these are not factors.

So, back to our mischievous candidate. We have learned that the factors of 34 are 1, 2, 17, and 34. It seems like his best possibility would be to have two jobs on his resume at 17 months each. Otherwise, it will appear poorly. He already doesn’t want just one job on his resume. However, he should have 17 or 34 jobs on his resume because that would be way too many. So, 2 is the best answer.

Challenging Questions

As a pilot, Henry looked at his schedule for the next month. He has a 34-city flights schedule. Henry likes to travel to a certain amount of cities each week for that month. Is that a possibility for Henry to fly to a specific amount of cities each week or will there be a different amount for one or more weeks? Use the factors of 34 to find out.

Answer

That would not be possible. The reason is that 4, which is the number of weeks in a month, is not a factor of 34. Instead, it would have to be a remainder in which one or more weeks had more cities to travel to.

A builder owns a plot of land that he wants to develop into a subdivision. He wants to build 34 houses in this subdivision. In what ways can he design the subdivision in which he will have an equal number of houses on each street. Think about how many streets he would need in the subdivision and how many houses would be on each street. Explain your design using the factors of 34.

Answer

This is a perfect way to use factors of 34. There are only a few ways since there aren’t many factors of 34. The build could have 1 long street with 34 houses on it, but that doesn’t seem reasonable. It could also be 34 streets with one house on each street, but that doesn’t seem reasonable either. The only other possibilities would be to have 2 streets with 17 houses on each of them or 17 streets with 2 houses on each of them. However, the best possibility would be the 2 streets with 17 houses on them.

There are 34 animals at the petting zoo. A class is taking a field trip to this petting zoo. The class will be divided into 5 groups. The petting zoo wants to divide the 34 animals, so that each group has an equal number of animals at the same time. Is this possible?

Answer

This is not a possibility since 5 is not a factor of 34. There would actually need to be one more animal in the group for that plan to take place because 5 is a factor of 35 but not 34. Instead, one group will need to have more animals in it than the others.

Frequently Asked Questions

No, 34 is not a prime number. A prime number is a number that can only be divisible by one and itself. This has to do with factoring because prime numbers only have 2 factors, whereas other numbers that are not prime numbers have more than 2 factors.

Besides one and the number itself, you can find the first factor by seeing if the number is an even number. If it is, then 2 is a factor as well as its factor partner. If it is not an even number, then you will need to see if the number 3 can divide into 34 without a remainder.

There really is no quick way to find the factors of a number. However, make sure you include 1 and 34 because 1 and the number itself will always be factors of a number. If the number is even, then 2 will be a factor. Find 2’s factor partner. In this case, it is 17. At this point, you only need to find the numbers between 3 and 16 that can be divide equally into 34 without having a remainder.