Do you know what these numbers have in common? 2, 4, 6, 8, 10, 12, 14…That’s right, they are even numbers. One important thing to remember that even numbers can do that other sets of numbers can’t do is that they are equally divisible by 2.

This is important to remember when trying to find the factors of a number. If it is an even number, then you will automatically have the number 2 as a factor.

Another good tip is that multiples of 3 have something in common too that’s important for finding factors. You guessed it. Those numbers can be divisible by 3. So, 3 would be a factor for those numbers.

A Small Number with Factors

The good thing to know is that the smaller numbers usually have fewer factors. So, if you get stuck trying to find all of the factors for a large number, it will probably take you longer. Let’s compare the number 6 with the number 1200.

Obviously, six will have 6 or fewer factors. However, 1200 could have as many as 1200. Of course, it won’t because there are numbers that won’t evenly divide into 1200, but you will have to spend time seeing if several numbers can divide into 1200 evenly.

Back to the number 6, let’s find the factors for this small number. Look at the tips below that you can use for all numbers and not just small numbers.

Tip 1: Start off with 1 and itself. (1,6)

Tip 2: Even numbers will always have 2 as a factor (1, 2, 6)

Also, remember its partner. $$2\;\times\;\_\_\_\_\;=\;6$$ Two and three are factors because 2 times 3 equals 6.

Tip 3: Multiples of 3 are evenly divisible by 3. (1, 2, 3, 6)

Also, remember its partner. $$3\;\times\;\_\_\_\_\;=\;6$$

After starting with these tips, you will need to find the other factors, but this will be a good start and knock some of the factors out of the way. For a small number like 6, this shouldn’t take you much time.

Factors of 6 are 1, 2, 3, and 6

Challenging Problems

A farmer has six sets of plant seeds to plant. He wants a neat garden, so think of how many rows and columns he will need to arrange his seeds. Use the factors of 6 to find out how many combinations he can use to arrange his garden.

Answer

We know that there are four factors for the number six. They are 1, 2, 3, and 6. Therefore, the farmer could arrange his garden with 1 row of 6 seeds or 6 columns of 1 seed in each column. The other two ways are to have 2 rows of 3 seeds or 3 rows of 2 seeds. Therefore, the farmer has four choices to arrange his garden.

You and your five friends are in line to ride a roller coaster at the county fair. So, there are 6 people total. You notice that 3 riders can comfortably fit into a seat on the roller coaster. Since the line is long, the roller coaster attendant will probably require that every seat is taken. How many seats will be used by you and your friends? Use the factors of 6 to answer the question.

Answer

In each seat, there will be 3 people. Since there are 6 people total, you can use your factors of 6 to find out how many seats the six people will use. Six divided by 3 equals 2. In other words, you could look at your list of factors for 6 and find the partner for 3.

At a restaurant stand, they are selling 6 types of sandwiches. They have the following types of sandwiches: Each week, you will try 2 different sandwiches, how many weeks will it take you to have sampled all of the sandwiches? Use the factors of 6 to find the answer.

Answer

It will take you 3 weeks to try all six sandwiches because you can divide 6 by 2. This will equal 3. The partner for 2 is 3 in the factors of 6.

With the situation above with the sandwiches, what would happen if you wanted to try 4 sandwiches per week? Can you explain how many weeks it would take you to sample all 6 of them?

Answer

In this situation, four is not a factor of 6. So, this means that there would be a remainder left over. Two sandwiches would be leftover. It would not take you a complete week to sample the rest of the sandwiches.

Frequently Asked Questions

Since 6 is such a small number, there are only a few steps to finding all of the factors for this number. However, these steps can be used with finding other factors for other numbers too. For 6, first, write down 1 and itself as the first factors for 6. Then since 6 is an even number, 2 will be a factor and its partner. 3 is 2’s partner, so 3 is also a factor of 6.

This is a common problem when finding the factors for a number. With the number 6, you start by seeing if 2 and 3 can evenly divide into 6. However, 6, the number itself, will be the highest factor. There are two numbers left to check, 4 and 5. Both 4 and 5 cannot be evenly divided into 6. There would be remainders. So, there are four factors for 6. Those are 1, 2, 3, and 6.

Factors of 6 can be used whenever you are dividing numbers into 6. Also, think about the many things that come in sixes. You can get a six-pack of soft drinks. There are many grocery items that come in groups of 6 like bagels, muffins, or cinnamon rolls. When you need to divide food among people, you may need to use the factors of 6.