Q: What are the factor combinations of the number 682,908?

 A:
Positive:   1 x 6829082 x 3414543 x 2276364 x 1707276 x 11381812 x 56909
Negative: -1 x -682908-2 x -341454-3 x -227636-4 x -170727-6 x -113818-12 x -56909


How do I find the factor combinations of the number 682,908?

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 682,908, 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.

1 682,908
-1 -682,908

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 682,908.

Example:
1 x 682,908 = 682,908
and
-1 x -682,908 = 682,908
Notice both answers equal 682,908

With that explanation out of the way, let's continue. Next, we take the number 682,908 and divide it by 2:

682,908 ÷ 2 = 341,454

If the quotient is a whole number, then 2 and 341,454 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 2 341,454 682,908
-1 -2 -341,454 -682,908

Now, we try dividing 682,908 by 3:

682,908 ÷ 3 = 227,636

If the quotient is a whole number, then 3 and 227,636 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 3 227,636 341,454 682,908
-1 -2 -3 -227,636 -341,454 -682,908

Let's try dividing by 4:

682,908 ÷ 4 = 170,727

If the quotient is a whole number, then 4 and 170,727 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 4 170,727 227,636 341,454 682,908
-1 -2 -3 -4 -170,727 -227,636 -341,454 682,908
Keep dividing by the next highest number until you cannot divide anymore.

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

123461256,909113,818170,727227,636341,454682,908
-1-2-3-4-6-12-56,909-113,818-170,727-227,636-341,454-682,908

More Examples

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