Q: What are the factor combinations of the number 209,556?

 A:
Positive:   1 x 2095562 x 1047783 x 698524 x 523896 x 349269 x 2328412 x 1746318 x 1164236 x 5821
Negative: -1 x -209556-2 x -104778-3 x -69852-4 x -52389-6 x -34926-9 x -23284-12 x -17463-18 x -11642-36 x -5821


How do I find the factor combinations of the number 209,556?

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 209,556, 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.

1 209,556
-1 -209,556

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 209,556.

Example:
1 x 209,556 = 209,556
and
-1 x -209,556 = 209,556
Notice both answers equal 209,556

With that explanation out of the way, let's continue. Next, we take the number 209,556 and divide it by 2:

209,556 ÷ 2 = 104,778

If the quotient is a whole number, then 2 and 104,778 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 2 104,778 209,556
-1 -2 -104,778 -209,556

Now, we try dividing 209,556 by 3:

209,556 ÷ 3 = 69,852

If the quotient is a whole number, then 3 and 69,852 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 69,852 104,778 209,556
-1 -2 -3 -69,852 -104,778 -209,556

Let's try dividing by 4:

209,556 ÷ 4 = 52,389

If the quotient is a whole number, then 4 and 52,389 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 52,389 69,852 104,778 209,556
-1 -2 -3 -4 -52,389 -69,852 -104,778 209,556
Keep dividing by the next highest number until you cannot divide anymore.

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

1234691218365,82111,64217,46323,28434,92652,38969,852104,778209,556
-1-2-3-4-6-9-12-18-36-5,821-11,642-17,463-23,284-34,926-52,389-69,852-104,778-209,556

More Examples

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