Q: What are the factor combinations of the number 404,631,359?

 A:
Positive:   1 x 40463135911 x 36784669131 x 3088789227 x 17825171237 x 3271071441 x 2807992497 x 16204713607 x 29737
Negative: -1 x -404631359-11 x -36784669-131 x -3088789-227 x -1782517-1237 x -327107-1441 x -280799-2497 x -162047-13607 x -29737


How do I find the factor combinations of the number 404,631,359?

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 404,631,359, 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.

1 404,631,359
-1 -404,631,359

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 404,631,359.

Example:
1 x 404,631,359 = 404,631,359
and
-1 x -404,631,359 = 404,631,359
Notice both answers equal 404,631,359

With that explanation out of the way, let's continue. Next, we take the number 404,631,359 and divide it by 2:

404,631,359 ÷ 2 = 202,315,679.5

If the quotient is a whole number, then 2 and 202,315,679.5 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:

1 404,631,359
-1 -404,631,359

Now, we try dividing 404,631,359 by 3:

404,631,359 ÷ 3 = 134,877,119.6667

If the quotient is a whole number, then 3 and 134,877,119.6667 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:

1 404,631,359
-1 -404,631,359

Let's try dividing by 4:

404,631,359 ÷ 4 = 101,157,839.75

If the quotient is a whole number, then 4 and 101,157,839.75 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:

1 404,631,359
-1 404,631,359
Keep dividing by the next highest number until you cannot divide anymore.

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

1111312271,2371,4412,49713,60729,737162,047280,799327,1071,782,5173,088,78936,784,669404,631,359
-1-11-131-227-1,237-1,441-2,497-13,607-29,737-162,047-280,799-327,107-1,782,517-3,088,789-36,784,669-404,631,359

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