Q: What are the factor combinations of the number 313,362?

 A:
Positive:   1 x 3133622 x 1566813 x 1044546 x 522277 x 447669 x 3481814 x 2238318 x 1740921 x 1492227 x 1160642 x 746154 x 580363 x 4974126 x 2487189 x 1658378 x 829
Negative: -1 x -313362-2 x -156681-3 x -104454-6 x -52227-7 x -44766-9 x -34818-14 x -22383-18 x -17409-21 x -14922-27 x -11606-42 x -7461-54 x -5803-63 x -4974-126 x -2487-189 x -1658-378 x -829


How do I find the factor combinations of the number 313,362?

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 313,362, 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.

1 313,362
-1 -313,362

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 313,362.

Example:
1 x 313,362 = 313,362
and
-1 x -313,362 = 313,362
Notice both answers equal 313,362

With that explanation out of the way, let's continue. Next, we take the number 313,362 and divide it by 2:

313,362 ÷ 2 = 156,681

If the quotient is a whole number, then 2 and 156,681 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 2 156,681 313,362
-1 -2 -156,681 -313,362

Now, we try dividing 313,362 by 3:

313,362 ÷ 3 = 104,454

If the quotient is a whole number, then 3 and 104,454 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 3 104,454 156,681 313,362
-1 -2 -3 -104,454 -156,681 -313,362

Let's try dividing by 4:

313,362 ÷ 4 = 78,340.5

If the quotient is a whole number, then 4 and 78,340.5 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 3 104,454 156,681 313,362
-1 -2 -3 -104,454 -156,681 313,362
Keep dividing by the next highest number until you cannot divide anymore.

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

123679141821274254631261893788291,6582,4874,9745,8037,46111,60614,92217,40922,38334,81844,76652,227104,454156,681313,362
-1-2-3-6-7-9-14-18-21-27-42-54-63-126-189-378-829-1,658-2,487-4,974-5,803-7,461-11,606-14,922-17,409-22,383-34,818-44,766-52,227-104,454-156,681-313,362

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