Q: What are the factor combinations of the number 310,908?

 A:
Positive:   1 x 3109082 x 1554543 x 1036364 x 777276 x 5181812 x 2590913 x 2391626 x 1195839 x 797252 x 597978 x 3986156 x 1993
Negative: -1 x -310908-2 x -155454-3 x -103636-4 x -77727-6 x -51818-12 x -25909-13 x -23916-26 x -11958-39 x -7972-52 x -5979-78 x -3986-156 x -1993


How do I find the factor combinations of the number 310,908?

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 310,908, 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.

1 310,908
-1 -310,908

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 310,908.

Example:
1 x 310,908 = 310,908
and
-1 x -310,908 = 310,908
Notice both answers equal 310,908

With that explanation out of the way, let's continue. Next, we take the number 310,908 and divide it by 2:

310,908 ÷ 2 = 155,454

If the quotient is a whole number, then 2 and 155,454 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 2 155,454 310,908
-1 -2 -155,454 -310,908

Now, we try dividing 310,908 by 3:

310,908 ÷ 3 = 103,636

If the quotient is a whole number, then 3 and 103,636 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 3 103,636 155,454 310,908
-1 -2 -3 -103,636 -155,454 -310,908

Let's try dividing by 4:

310,908 ÷ 4 = 77,727

If the quotient is a whole number, then 4 and 77,727 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 77,727 103,636 155,454 310,908
-1 -2 -3 -4 -77,727 -103,636 -155,454 310,908
Keep dividing by the next highest number until you cannot divide anymore.

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

123461213263952781561,9933,9865,9797,97211,95823,91625,90951,81877,727103,636155,454310,908
-1-2-3-4-6-12-13-26-39-52-78-156-1,993-3,986-5,979-7,972-11,958-23,916-25,909-51,818-77,727-103,636-155,454-310,908

More Examples

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