Factors of 34

Posted on24 April 2022

Introduction

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.

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.