Q: What are the factor combinations of the number 404,022,323?

 A:
Positive:   1 x 40402232317 x 2376601941 x 9854203449 x 899827697 x 5796591291 x 3129537633 x 5293118409 x 21947
Negative: -1 x -404022323-17 x -23766019-41 x -9854203-449 x -899827-697 x -579659-1291 x -312953-7633 x -52931-18409 x -21947


How do I find the factor combinations of the number 404,022,323?

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 404,022,323, 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.

1 404,022,323
-1 -404,022,323

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 404,022,323.

Example:
1 x 404,022,323 = 404,022,323
and
-1 x -404,022,323 = 404,022,323
Notice both answers equal 404,022,323

With that explanation out of the way, let's continue. Next, we take the number 404,022,323 and divide it by 2:

404,022,323 ÷ 2 = 202,011,161.5

If the quotient is a whole number, then 2 and 202,011,161.5 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:

1 404,022,323
-1 -404,022,323

Now, we try dividing 404,022,323 by 3:

404,022,323 ÷ 3 = 134,674,107.6667

If the quotient is a whole number, then 3 and 134,674,107.6667 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:

1 404,022,323
-1 -404,022,323

Let's try dividing by 4:

404,022,323 ÷ 4 = 101,005,580.75

If the quotient is a whole number, then 4 and 101,005,580.75 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:

1 404,022,323
-1 404,022,323
Keep dividing by the next highest number until you cannot divide anymore.

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

117414496971,2917,63318,40921,94752,931312,953579,659899,8279,854,20323,766,019404,022,323
-1-17-41-449-697-1,291-7,633-18,409-21,947-52,931-312,953-579,659-899,827-9,854,203-23,766,019-404,022,323

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