Q: What are the factor combinations of the number 210,043,309?

 A:
Positive:   1 x 2100433097 x 3000618719 x 11054911133 x 1579273241 x 8715491687 x 1245074579 x 458716553 x 32053
Negative: -1 x -210043309-7 x -30006187-19 x -11054911-133 x -1579273-241 x -871549-1687 x -124507-4579 x -45871-6553 x -32053


How do I find the factor combinations of the number 210,043,309?

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 210,043,309, 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.

1 210,043,309
-1 -210,043,309

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 210,043,309.

Example:
1 x 210,043,309 = 210,043,309
and
-1 x -210,043,309 = 210,043,309
Notice both answers equal 210,043,309

With that explanation out of the way, let's continue. Next, we take the number 210,043,309 and divide it by 2:

210,043,309 ÷ 2 = 105,021,654.5

If the quotient is a whole number, then 2 and 105,021,654.5 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:

1 210,043,309
-1 -210,043,309

Now, we try dividing 210,043,309 by 3:

210,043,309 ÷ 3 = 70,014,436.3333

If the quotient is a whole number, then 3 and 70,014,436.3333 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:

1 210,043,309
-1 -210,043,309

Let's try dividing by 4:

210,043,309 ÷ 4 = 52,510,827.25

If the quotient is a whole number, then 4 and 52,510,827.25 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:

1 210,043,309
-1 210,043,309
Keep dividing by the next highest number until you cannot divide anymore.

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

17191332411,6874,5796,55332,05345,871124,507871,5491,579,27311,054,91130,006,187210,043,309
-1-7-19-133-241-1,687-4,579-6,553-32,053-45,871-124,507-871,549-1,579,273-11,054,911-30,006,187-210,043,309

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