Q: What are the factor combinations of the number 32,568?

 A:
Positive:   1 x 325682 x 162843 x 108564 x 81426 x 54288 x 407112 x 271423 x 141624 x 135746 x 70859 x 55269 x 47292 x 354118 x 276138 x 236177 x 184
Negative: -1 x -32568-2 x -16284-3 x -10856-4 x -8142-6 x -5428-8 x -4071-12 x -2714-23 x -1416-24 x -1357-46 x -708-59 x -552-69 x -472-92 x -354-118 x -276-138 x -236-177 x -184


How do I find the factor combinations of the number 32,568?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 32,568, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 32,568
-1 -32,568

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 32,568.

Example:
1 x 32,568 = 32,568
and
-1 x -32,568 = 32,568
Notice both answers equal 32,568

With that explanation out of the way, let's continue. Next, we take the number 32,568 and divide it by 2:

32,568 ÷ 2 = 16,284

If the quotient is a whole number, then 2 and 16,284 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 16,284 32,568
-1 -2 -16,284 -32,568

Now, we try dividing 32,568 by 3:

32,568 ÷ 3 = 10,856

If the quotient is a whole number, then 3 and 10,856 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 10,856 16,284 32,568
-1 -2 -3 -10,856 -16,284 -32,568

Let's try dividing by 4:

32,568 ÷ 4 = 8,142

If the quotient is a whole number, then 4 and 8,142 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 8,142 10,856 16,284 32,568
-1 -2 -3 -4 -8,142 -10,856 -16,284 32,568
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

123468122324465969921181381771842362763544725527081,3571,4162,7144,0715,4288,14210,85616,28432,568
-1-2-3-4-6-8-12-23-24-46-59-69-92-118-138-177-184-236-276-354-472-552-708-1,357-1,416-2,714-4,071-5,428-8,142-10,856-16,284-32,568

More Examples

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