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A bunch of boys goes to the local basketball court in their neighborhood to play a pick-up game. Nine boys show up. There is a problem with this. Can you figure out what the problem will be?
The group of 9 boys can’t be divided equally in half by 2 because 9 is an odd number. Two is not a factor of any odd numbers. So, you can skip 2 when you are figuring out the factors of an odd number. Only even numbers have 2 as a factor. Now, back to the basketball game.
When the group of boys tries to divide the team in half, there will be one boy left over. So, one team will have more boys on it than the other, which will be unfair. One boy will either have to sit out for the game, or they will have to play with uneven numbered teams.
Maybe there is a solution to this problem. It may not be perfect, but it is a solution. Divide the group by 3. Then that will make 3 groups of 3 boys.
Instead of just one boy sitting out, all three groups on one team will either sit out, or they will practice on the other side of the court while the other two teams of 3 play against each other on the other side of the court. The reason this is a solution is because 3 is a factor of 9.
There will not be a remainder when you divide 3 into 9.
Let’s find all of the factors for the number 9. Certainly, 1 and 9 are factors just like they are for every number. We already ruled out 2, but from the basketball scenario, we know that 3 is a factor. However, just like all of the other factors, we have to find its partner.
So, we divide 9 by 3 which is 3. You do not need to write out the factors as 1, 3, 3, 9. There is no need to repeat the factor. Instead, the factors are 1, 3, and 9. The number 3 is the factor and its partner.
This makes it easy because once we find the factor and its partner, then we don’t have to look any further for more factors.
However, if you want to make sure that there are not any more factors for 9, you can do so. Numbers 4, 5, 6, 7, and 8 are not factors because they will not equally divide into 9 without getting a remainder. You can tell quickly by multiplying 4 times the lowest number 2 that you could use.
This would equal 8 which would cause you to get a remainder if you multiplied the next higher number, 3 to 4. If you choose to try 5, then you will see that 5 times 2 is ten which is over your number. At this point, you can stop trying because five has already shown that this factor is already higher than your original number.
Factors of 9 are 1, 3, and 9
Your final exam for chemistry is coming up soon. You decide to study your entire textbook which contains 9 chapters. You know that you can’t study chapter after chapter without getting to take a break. So, you need to evenly divide the textbook into sections and with a break after each section. With the factors of 9, how will you divide up the textbook into sections? Explain how you will go about doing that.
Since there are only 3 factors for 9, you do not have a lot to choose from. You already know that you can’t study all 9 chapters at once, so we can rule out that factor. Now, we have 1 and 3 left. If you take a break after each chapter, then this may take you too long. That doesn’t seem like a good idea. The best idea would be to divide the textbook into 3 chapters. After every 3 chapters, you will take a break. Then you will have 3 sections of 3 chapters.
In the game of billiards or pool, there is a game you can play called 9-ball. You only use the balls numbered 1 through 9. The goal is the sink the balls into the pockets in order from 1 to 9. Sounds easy, right? Well, not really, unless you are a pool shark. However, let’s pretend that you are that pool shark. You can actually sink two balls into a pocket by hitting one ball into another. Will this work to sink two balls into the pocket for each turn that you have without having any balls left over? Explain your thoughts using the factors of 9.
Unfortunately, this will not work because 2 is not a factor of 9. To illustrate this, you first sink balls 1 and 2 into their pockets. Then, you sink balls 3 and 4 followed by 5 and 6. You sink balls 7 and 8. Now, you have one ball left over, the “nine” ball.
The United States Supreme Court has 9 court justices at one time. If they are voting on cases, the justices must vote for or against them. If they added a choice to abstain, what problem would this cause the justices and their cases? Think about the factors of 9.
If there were 3 choices, this would cause a problem because then 3 is a factor of 9. This means there will not be any justice left over. It could end in a tie. Three justices could vote for it, three could vote against it, and three could abstain.
To find the factors of 9, start with one and itself, 9. Then know that you can skip 2 because 9 is not an even number because it is an odd number. Next, divide 9 by 3. It is a factor for 9 because 3 times 3 equals nine. There is not a remainder. Also, you can stop there because 3 is a factor, and 3 is also its partner.
Whenever there are groups of nine used, then you will need to know the factors of 9 especially when you do not want a remainder.
There are 3 factors for the number 9.
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