Q: What are the factor combinations of the number 310,640,705?

 A:
Positive:   1 x 3106407055 x 6212814189 x 3490345445 x 698069787 x 394715887 x 3502153935 x 789434435 x 70043
Negative: -1 x -310640705-5 x -62128141-89 x -3490345-445 x -698069-787 x -394715-887 x -350215-3935 x -78943-4435 x -70043


How do I find the factor combinations of the number 310,640,705?

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 310,640,705, 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.

1 310,640,705
-1 -310,640,705

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 310,640,705.

Example:
1 x 310,640,705 = 310,640,705
and
-1 x -310,640,705 = 310,640,705
Notice both answers equal 310,640,705

With that explanation out of the way, let's continue. Next, we take the number 310,640,705 and divide it by 2:

310,640,705 ÷ 2 = 155,320,352.5

If the quotient is a whole number, then 2 and 155,320,352.5 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:

1 310,640,705
-1 -310,640,705

Now, we try dividing 310,640,705 by 3:

310,640,705 ÷ 3 = 103,546,901.6667

If the quotient is a whole number, then 3 and 103,546,901.6667 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:

1 310,640,705
-1 -310,640,705

Let's try dividing by 4:

310,640,705 ÷ 4 = 77,660,176.25

If the quotient is a whole number, then 4 and 77,660,176.25 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:

1 310,640,705
-1 310,640,705
Keep dividing by the next highest number until you cannot divide anymore.

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

15894457878873,9354,43570,04378,943350,215394,715698,0693,490,34562,128,141310,640,705
-1-5-89-445-787-887-3,935-4,435-70,043-78,943-350,215-394,715-698,069-3,490,345-62,128,141-310,640,705

More Examples

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