Kevin is a procrastinator. He puts things off all the time, especially his homework. His English teacher, Mr. Simmons, asked the class to read a novel. Of course, Kevin was assigned this task many weeks ago.

However, due to Kevin’s nature, he waits until the last minute to start the novel. He realizes that in order to get the book finished he will have to skim the pages. He has already divided the 300-paged book into sections of 30 pages each.

Now, he wants to break up the 30 pages into smaller sections and write notes every so often about that group of pages.

How could he evenly divide up each group of 30 pages? What are the possibilities?

The best way to find all possible options would be to find the factors of 30.

Factors of 30

Let’s look at the factors of 8. We can use the steps to find all of the factors of 8.

The way to go about doing this is to divide the number into 30 to see if there is a remainder. Let’s look at the next number, 3.

Based on this problem, 3 divides evenly into 30. So, 3 and 10 are factors. Now, we need to see if any numbers between 4 and 9 are factors. We will do the same. Let’s divide 4 into 30.

Four would not be a factor of 30 because there is a remainder of 2. Seven would also not be a factor of 30 because it would have the same remainder.

If we checked 5, 6, 7, 8 and 9, we would find out that five and six are factor partners because they both evenly divide into 30 without a remainder. The others do not.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Now, back to Kevin’s problem with his assignment. He could divide the 30 pages into groups of 2 groups of 15, 15 groups of 2, 5 groups of 6, 6 groups of 5, 3 groups of 10 or 10 groups of 3. He could also have a lot of little groups by having 30 groups of 1 page each or a big group of 1 group of 30 pages.

Challenging Questions

In math class, you find that there is a 30-degree angle. You must measure the angle and section off the angle. Using your protractor, you find that there are a number of ways to section off angle. Find the factors of 30 to find how many sections you can have.

Answer

The number 30 has 8 factors. That means there are 4 sets of factors because each factor has a partner. When multiplied together, the factor and its partner would equal 30. In this problem, a 30-degree angle could be divided into 6 different ways. It could be divided into 30 sections of 1 degree each or leave as 1 big angle. It could also be divided into 2 sections of 15 degrees each or 15 sections with 2 degrees each. You could divide it into 3 sections of 10 degrees each or 10 sections of 3 degrees each. Finally, you could have 5 sections with 6 degrees each or 6 sections with 5 degrees each.

A biography of a 30-year old is divided into 10 chapters. How many years would each chapter cover if each chapter covers the same number of years? Make sure to use the factors of 30 to find and explain your answer.

Answer

Each chapter would include 3 years of the person’s life. Ten is a factor of 30, so we need to find its factor partner. Ten’s factor partner is 3, so that is how we know that each chapter would focus on 3 years of the person’s life.

A health nut takes 30 vitamins a week. There are 6 different kinds of vitamins. How many of each vitamin does the health nut take per week. Use the factors of 30 to find and explain your answer.

Answer

The factors of 30 are 1, 2, 3, 5, 6, 10. 15, and 30. So, let’s find 6’s factor partner. That means what number multiplied to 6 equals 30. That would be 5. So, there would be five vitamins of each of the 6 kinds of vitamins taken by this person.

Frequently Asked Questions

The higher the number is the less likely you will find groups of items that normally contain that amount. There are not a lot of groups that are known for having 30 objects or items in them. However, that is not to say that there are none. There is a 30-60-90 triangle. So, one of the angles is known for measuring 30 degrees. Also, there is a 30-day forecast as there are usually 30 days in a month.

The best way to make sure you have all of the factors is to multiply each number between 1 and 30. Do not skip numbers if you want to double check.

The steps include starting with 1 and itself, 30. Then, you will know that 2 is a factor because 30 is an even number. We need to find its factor partner. So, 2’s factor partner is 15. Then we need to see if numbers 3 through 14 are factors of 30 and can equally be divided into 32 without having a remainder. In this case, 3, 5, 6, 10 are also factors of 32.