Q: What are the factor combinations of the number 803,658?

 A:
Positive:   1 x 8036582 x 4018293 x 2678866 x 13394317 x 4727434 x 2363751 x 15758102 x 7879
Negative: -1 x -803658-2 x -401829-3 x -267886-6 x -133943-17 x -47274-34 x -23637-51 x -15758-102 x -7879


How do I find the factor combinations of the number 803,658?

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 803,658, 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.

1 803,658
-1 -803,658

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 803,658.

Example:
1 x 803,658 = 803,658
and
-1 x -803,658 = 803,658
Notice both answers equal 803,658

With that explanation out of the way, let's continue. Next, we take the number 803,658 and divide it by 2:

803,658 ÷ 2 = 401,829

If the quotient is a whole number, then 2 and 401,829 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 2 401,829 803,658
-1 -2 -401,829 -803,658

Now, we try dividing 803,658 by 3:

803,658 ÷ 3 = 267,886

If the quotient is a whole number, then 3 and 267,886 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 3 267,886 401,829 803,658
-1 -2 -3 -267,886 -401,829 -803,658

Let's try dividing by 4:

803,658 ÷ 4 = 200,914.5

If the quotient is a whole number, then 4 and 200,914.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 2 3 267,886 401,829 803,658
-1 -2 -3 -267,886 -401,829 803,658
Keep dividing by the next highest number until you cannot divide anymore.

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

12361734511027,87915,75823,63747,274133,943267,886401,829803,658
-1-2-3-6-17-34-51-102-7,879-15,758-23,637-47,274-133,943-267,886-401,829-803,658

More Examples

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