Q: What are the factor combinations of the number 809,304?

 A:
Positive:   1 x 8093042 x 4046523 x 2697684 x 2023266 x 1348848 x 10116312 x 6744224 x 33721
Negative: -1 x -809304-2 x -404652-3 x -269768-4 x -202326-6 x -134884-8 x -101163-12 x -67442-24 x -33721


How do I find the factor combinations of the number 809,304?

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 809,304, 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.

1 809,304
-1 -809,304

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 809,304.

Example:
1 x 809,304 = 809,304
and
-1 x -809,304 = 809,304
Notice both answers equal 809,304

With that explanation out of the way, let's continue. Next, we take the number 809,304 and divide it by 2:

809,304 ÷ 2 = 404,652

If the quotient is a whole number, then 2 and 404,652 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 2 404,652 809,304
-1 -2 -404,652 -809,304

Now, we try dividing 809,304 by 3:

809,304 ÷ 3 = 269,768

If the quotient is a whole number, then 3 and 269,768 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 3 269,768 404,652 809,304
-1 -2 -3 -269,768 -404,652 -809,304

Let's try dividing by 4:

809,304 ÷ 4 = 202,326

If the quotient is a whole number, then 4 and 202,326 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 4 202,326 269,768 404,652 809,304
-1 -2 -3 -4 -202,326 -269,768 -404,652 809,304
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122433,72167,442101,163134,884202,326269,768404,652809,304
-1-2-3-4-6-8-12-24-33,721-67,442-101,163-134,884-202,326-269,768-404,652-809,304

More Examples

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