You grab your pack of 8 water bottles out of the fridge. You want to hand out an equal amount of water to your family members outside who are raking leaves. Not that it matters, but if everyone has an equal number of water bottles, then there won’t be any arguing among the children.

Think about what other information you need to know to determine how many water bottles to hand out to each member of your family.

You will need to know the number of family members, including yourself, are working outside raking the leaves. Once you have that number, then you can use the factors of 8 to find out how many water bottles each person will get. In order for everyone to get an equal number of water bottles, the number of people would have to be a factor of 8.

The Factors of 8

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

Let’s try 3.

Three does not divide equally into 8. There is a remainder of 2.

Let’s try 5 next. As you can see below, 5 cannot divide equally into 8 either. There is a remainder of 3.

Let’s try 6 next.

Eight is not evenly divisible by 6 either. Two is left over. So, the last number to try is 7. Seven isn’t a factor either. There would be a remainder of one. You may be able to easily see that these numbers cannot divide equally into 8 because the numbers are too high.

For instance, 5, 6, and 7 are so close to 8 that you can immediately see there will be a remainder.

Factors for 8 are 1, 2, 4, 8

Challenging Questions

In a craft, you are making a paper flower with 8 petals. To make it a colorful flower that has a pattern to the petals, you want the petals to have at least 2 colors, but then have an equal number of petals for each color. How many combinations could you have? Think of the factors of 8.

Answer

There are only 2 combinations if you want to use at least 2 colors. Since 2 and 4 are factors of 8, then you could have 2 colors with 4 petals in each color or 4 colors with 2 petals in each color.

A songwriter is writing a song, who loves to play two notes in the octave at one time. If she wants to use all 8 notes first before repeating any, how many note sets will she use? See if you can figure out the answer with the factors of 8.

Answer

There are 8 notes in an octave. Since the songwriter wants to play two notes within the octave at one time and do this without repeating any notes, you will need to divide 8 by 2. This will provide the songwriter with 4 notes sets. She will play four sets of notes before starting over or beginning to repeat notes.

You baked an apple pie for your party. After the pie has cooled, you go ahead and cut the pie quickly into 8 equal pieces. However, you are not sure exactly how many people will be coming to your party. It is supposed to be a small party, but some people might bring friends. Explain using your knowledge of the factors of 8 how you will be able to serve the same number of pieces of pie to you and your friends at your party. Describe the numbers of people who could be at the party in order for this to work.

Answer

There are only certain amounts of people who could be there for each person to receive an equal number of pieces of pie as the other members of the party without having any leftovers. We will assume that everyone loves apple pie, and everyone wants as much of the pie as possible. Using the factors of 8, which are 1, 2, 4, and 8, this would show the number of people who could be at the party for this situation to work. Sadly, if no one showed up, then you would be the only person at the party, and you could eat the whole pie. If one other person came to the party, so you would have 2 people at the party, each person would get 4 pieces of pie. If 3 people showed up, then there would be 4 people at the party. Each of the 4 people would receive 2 pieces of pie. Finally, if seven more people showed up for a total of 8 people at the party, then each person would get one piece of pie.

Frequently Asked Questions

There are several things that sometimes come in groups of 8. Certain types of flowers like Clematis have 8 petals. Other things would be a stop sign has 8 sides, batteries sometimes come in packs of 8, and there are 8 hours in a work day. When you have to divide or group items within a group of 8, then you will need to know the factors of 8.

To find the factors of 8, see which numbers up to 8 can divide equally into 8 without having a remainder.

The best way to make sure that you have found all of the factors of 8 would be to first find out if 2 and 3 equally divide into 8 without a remainder. Then find their partners. Two’s partner is 4. Three does not equally divide into 8. Now, you know you are done because once you start finding a factor and its partner, then you only have to look at your two inner numbers once you line up your factors in numerical order. Therefore, you have 2 and 4. Those are your inner numbers. The only number that is left is 3. We found out that 3 is not a factor, so there are no other numbers left to see if they are factors of 8.