Factors of 76

Introduction

The United States declared its independence in 1776. From the turn of the century to the time of this declarations, many events took place during these 76 years. There are probably too many to count. As a historian, Pete needs to create a timeline of events for these 76 years showing how these events led to the declaration of the United States. To do this, he must divide the timeline equally among the 76 years. Help Pete to determine the best way to do this. He will need to use the factors of 76 to find how many divisions he will need for his timeline. Remember, there will be some logical and reasonable choices, but some unreasonable ones too. This means that not all of the factors can be used. Some factors will have to be ruled out.

76 – What are all the factors?

First, we need to look at the factors of 76. Use the steps to find all of the factors of 76. It is important to find all factors of 76 for many reasons. For Pete’s timeline from above, you will need to find the more reasonable factors that you could use in the timeline. Therefore, not all factors will be used in the timeline situation. However, it is best to find all of them. Then look to see if the factor is a reasonable or not for this situation.

To do this, divide the number into 76 to see if there is a remainder. Let’s look at the next number, 3.

Three does not divide equally into 76 because there would be a remainder. Now, we need to see if 4 divides into 76 equally without having a remainder. It does. We then need to find 4’s factor partner for 76. Its factor partner is 19.

So, 4 is a factor of 76 because there is no remainder. Nineteen is 4’s factor partner. So, both four and nineteen are both factors of 76. Five is not a factor of 76 because it does not divide equally into 76. It has a remainder.

Now, we need to check 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18. These numbers are not factors of 76 because they have a remainder when divided into 76.

So, we have figured out that 76 has 6 factors. These factors are 1, 2, 4, 19, 38, and 76.

Now, back to the timeline situation. Pete needs to divide his timeline into equally amounts of years just like any other timeline. He wants each space in between the events to have an equal amount of years. So, that is where the factors come into place. We can rule out 1 and 76 because 1 is not enough years and 76 is too many divisions. Therefore, we must look at the rest of the factors. Two and 38 also can be ruled out because two is also not enough divisions and 38 is too many divisions. So, Pete could divide the area into 4 divisions of 19 years each or 19 divisions of 4 years each. I believe the best answer would be to divide the timeline into 4 divisions of 19 years each. This seems to be the most reasonable for a timeline.

Challenging Questions