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2. Copyright©2001 Lynda Greene
Factors & Multiples
Copyright©2001 Lynda Greene
Factors of numbers

3. Introduction to Factors What are they and how do I find them?

4. What are factors and how do I find them?
Example: Say you want to find the factors of 8.
The factors of 8 are all the numbers that will divide into 8 evenly.
(In other words, they do not have a remainder)
So take the numbers from 1 to 8 and divide 8 by each of them. 8 4 2
remainder
1) 8
2) 8
3) 8
4) 8
If you get an answer with a remainder, the number you divided by is not a factor of 8, so cross out these answers. 1
remainder
remainder
remainder
5) 8
6) 8
7) 8
8) 8
Now let’s look at the numbers that are left

5. The numbers on the left are the factors of 8, factors: 1, 2, 4 and 8
1) 8
8) 8
2) 8
4) 8 8 4 2 1
But, did you notice that the numbers on the top and the numbers you divided by (on the left) are the same?
That’s because we are finding the factors two at a time,
The number on the left and the number on top
are both factors of 8.
So to save time we don’t have to divide by every number from 1 to 8, we can go halfway and stop.

6. 8 All the factors of 8 are right here in this little box.
How do we know when we have gotten halfway and can stop?
If you write the factors of the number using the following system,
you can see where your stopping point will be.
1) Write the number with two little branches below it 8
2) Starting with ‘1 x 8’
Write all the pairs of factors
that divide evenly into 8
All the factors
of 8 are right here in this little box.
1 x 8
2 x 4
4 x 2
8 x 1
3) This is where they
start to repeat, STOP HERE!
You don’t need to write these repeating numbers down

7. 12 32 81 48 Practice: Find the factors of the following numbers 1 x 48
Read the factors
in this order
We can stop checking numbers
as soon as we reach this number
1 x 48
2 x 24
3 x 16
4 x 12
5 : remainder
6 x 8
7 : remainder
1 x 12
2 x 6
3 x 4
1 x 32
2 x 16
4 x 8
1 x 81
3 x 27
9 x 9
Down the left side
Up the right side
Here’s where the
numbers start to
repeat 4 x 3, etc.
so stop here.
5 : remainder
6 : remainder
7 : remainder
8 x 4(repeat)
You can stop here
since there are no
more numbers
between these two
factors on the bottom
Stop, since the
next number is 8
Make sure you check all the numbers up to the number on the bottom right, this is where they start to repeat.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 81: 1, 3, 9, 27, 81
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

8. Practice Problems: (Hit enter to see the answers)
Find all the possible Factors of the following numbers
1) ) 64
2) ) 75
3) ) 110
4) ) 83
Answers:
1) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
2) 1, 2, 3, 6, 13, 26, 39, 78
3) 1, 59 (prime number)
4) 1, 2, 4, 8, 16, 32
5) 1, 2, 4, 8, 16, 32, 64
6) 1, 3, 5, 15, 25, 75
7) 1, 2, 5, 10, 11, 22, 55, 110
8) 1, 83 (prime)

9. Questions? send e-mail to: lgreene1@satx.rr.com
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