Learning About Factors

 

Before starting to work on division, it is helpful to think about FACTORS. Factors are the things that multiply to give a PRODUCT (Product is what we call the ANSWER in a multiplication problem).

 

Let's start with 6. What multiplication facts multiply to give you 6? With any number, you can always take the number and multiply it by one to get self. In other words: 6 X 1 = 6. What other fact gives 6 as an answer? Our next check should be if the number is an EVEN number. If it is an EVEN number then you know that 2 will be a factor. In the case of 6, we get 2 X 3 = 6. These are our factors of 6.

 

6 = 1X6

6 = 2X3

 

Let's test ourselves to see if we know which number will have a factor of 2. If the number is EVEN, 2 is a factor. Divide it in half to find the other factor.

 

Write down the numbers that have 2 as a factor, then write the other factor. If 2 is not a factor, write ODD

 

Number

Factor

12

Answer

15

Answer

20

Answer

9

Answer

18

Answer

40

Answer

14

Answer

 

 

To determine if 5 is a factor, we only have to look to the last digit of the number, if it is a 5 or a 0, then 5 will be a factor. Think about counting by 5's: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. All the numbers end in a 5 or a 0.

 

Let's find the factors of 20:

First, we can see if 2 is a factor. Yes, 20 is even, so 2 is a factor. If we divide 20 in half we get 10, therefore 2 X 10 is one way to get 20.

Next, we see that 5 must be a factor because 20 ends in a zero. Do you remember what times 5 gave us 20? If not, you can count by 5's until you get there and see how many numbers you had to count: 5, 10, 15, 20. You had to count 4 times to get to 20, so 4 X 5 = 20.

Our factors of 20 are going to be: 1 X 20, 2 X 10, and 4 X 5.

 

To deterine if 10 is a factor, think about what the pattern is when you count by 10: 10, 20, 30, 40, 50, ... You can see that all the numbers end in a 0. Remember how you learned to multiply by 10? You just added a zero to the number. 4 X 10 = 40. (Add a zero after the 4).

 

Let's find the factors of 30:

First, 30 is even so 2 must be a factor. Divide 30 in half and you can see that 15 X 2 = 30.

Since 30 ends in a 0, it must also have 5 as a factor. Count by 5's to see how many 5's are in 30: 5, 10, 15, 20, 25, 30. There are 6 numbers so 5 X 6 = 30.

Now we also notice that 30 ends in a zero, so 10 must be a factor. We can see that 3 X 10 = 30.

Let's see all our factors: 1 X 30, 2 X 15, 3 X 10, 5 X 6.

 

Let's just practice with our 2's, 5's and 10's right now.

 

Number

2 Factor

5 Factor

10 Factor

10

2 X 5

5 X 2

10 X 1

15

ODD

5 X 3

Doesn't end in 0

20

2 X 10

5 X 4

10 X 2

30

2 X 15

5 X 6

10 X 3

40

2 X 20

5 X 8

10 X 4

 

Let's now think about 4's for a minute. To find 6 X 4, we doubled 6 (and got 12) and then doubled again (and got 24). To go BACKWARDS, we can take HALF and then take HALF AGAIN.

 

Let's start with 24. Take half, you get 12, take half again, you get 6. So we know that 6 X 4 = 24.

Let try 32. Taking half is harder but we get 16. Half of 16 is 8. So we can see that 4 is a factor of 32.

What happens if 4 is not a factor. Let's see what happens when we have 30. Take half, we get 15, when we go to take half again, we can't 15 is ODD. So 4 cannot be a factor of 30.

 


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