Factors of 30

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