Q: What are the factor combinations of the number 304,230,031?

 A:
Positive:   1 x 3042300317 x 4346143343 x 7075117239 x 1272929301 x 10107311673 x 1818474229 x 7193910277 x 29603
Negative: -1 x -304230031-7 x -43461433-43 x -7075117-239 x -1272929-301 x -1010731-1673 x -181847-4229 x -71939-10277 x -29603


How do I find the factor combinations of the number 304,230,031?

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 304,230,031, 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.

1 304,230,031
-1 -304,230,031

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 304,230,031.

Example:
1 x 304,230,031 = 304,230,031
and
-1 x -304,230,031 = 304,230,031
Notice both answers equal 304,230,031

With that explanation out of the way, let's continue. Next, we take the number 304,230,031 and divide it by 2:

304,230,031 ÷ 2 = 152,115,015.5

If the quotient is a whole number, then 2 and 152,115,015.5 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:

1 304,230,031
-1 -304,230,031

Now, we try dividing 304,230,031 by 3:

304,230,031 ÷ 3 = 101,410,010.3333

If the quotient is a whole number, then 3 and 101,410,010.3333 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:

1 304,230,031
-1 -304,230,031

Let's try dividing by 4:

304,230,031 ÷ 4 = 76,057,507.75

If the quotient is a whole number, then 4 and 76,057,507.75 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:

1 304,230,031
-1 304,230,031
Keep dividing by the next highest number until you cannot divide anymore.

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

17432393011,6734,22910,27729,60371,939181,8471,010,7311,272,9297,075,11743,461,433304,230,031
-1-7-43-239-301-1,673-4,229-10,277-29,603-71,939-181,847-1,010,731-1,272,929-7,075,117-43,461,433-304,230,031

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