Q: What are the factor combinations of the number 310,705,021?

 A:
Positive:   1 x 31070502111 x 2824591137 x 8397433407 x 763403
Negative: -1 x -310705021-11 x -28245911-37 x -8397433-407 x -763403


How do I find the factor combinations of the number 310,705,021?

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 310,705,021, 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.

1 310,705,021
-1 -310,705,021

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 310,705,021.

Example:
1 x 310,705,021 = 310,705,021
and
-1 x -310,705,021 = 310,705,021
Notice both answers equal 310,705,021

With that explanation out of the way, let's continue. Next, we take the number 310,705,021 and divide it by 2:

310,705,021 ÷ 2 = 155,352,510.5

If the quotient is a whole number, then 2 and 155,352,510.5 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:

1 310,705,021
-1 -310,705,021

Now, we try dividing 310,705,021 by 3:

310,705,021 ÷ 3 = 103,568,340.3333

If the quotient is a whole number, then 3 and 103,568,340.3333 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:

1 310,705,021
-1 -310,705,021

Let's try dividing by 4:

310,705,021 ÷ 4 = 77,676,255.25

If the quotient is a whole number, then 4 and 77,676,255.25 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:

1 310,705,021
-1 310,705,021
Keep dividing by the next highest number until you cannot divide anymore.

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

11137407763,4038,397,43328,245,911310,705,021
-1-11-37-407-763,403-8,397,433-28,245,911-310,705,021

More Examples

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