Q: What are the factor combinations of the number 404,004,131?

 A:
Positive:   1 x 40400413123 x 17565397131 x 30840013013 x 134087
Negative: -1 x -404004131-23 x -17565397-131 x -3084001-3013 x -134087


How do I find the factor combinations of the number 404,004,131?

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 404,004,131, 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.

1 404,004,131
-1 -404,004,131

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 404,004,131.

Example:
1 x 404,004,131 = 404,004,131
and
-1 x -404,004,131 = 404,004,131
Notice both answers equal 404,004,131

With that explanation out of the way, let's continue. Next, we take the number 404,004,131 and divide it by 2:

404,004,131 ÷ 2 = 202,002,065.5

If the quotient is a whole number, then 2 and 202,002,065.5 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:

1 404,004,131
-1 -404,004,131

Now, we try dividing 404,004,131 by 3:

404,004,131 ÷ 3 = 134,668,043.6667

If the quotient is a whole number, then 3 and 134,668,043.6667 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:

1 404,004,131
-1 -404,004,131

Let's try dividing by 4:

404,004,131 ÷ 4 = 101,001,032.75

If the quotient is a whole number, then 4 and 101,001,032.75 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:

1 404,004,131
-1 404,004,131
Keep dividing by the next highest number until you cannot divide anymore.

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

1231313,013134,0873,084,00117,565,397404,004,131
-1-23-131-3,013-134,087-3,084,001-17,565,397-404,004,131

More Examples

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