Factors of 9

Introduction

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.

3 Factors for 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.