Q: What are the factor combinations of the number 431,405,039?

 A:
Positive:   1 x 43140503913 x 3318500317 x 25376767221 x 1952059289 x 14927513757 x 114827
Negative: -1 x -431405039-13 x -33185003-17 x -25376767-221 x -1952059-289 x -1492751-3757 x -114827


How do I find the factor combinations of the number 431,405,039?

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 431,405,039, 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.

1 431,405,039
-1 -431,405,039

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 431,405,039.

Example:
1 x 431,405,039 = 431,405,039
and
-1 x -431,405,039 = 431,405,039
Notice both answers equal 431,405,039

With that explanation out of the way, let's continue. Next, we take the number 431,405,039 and divide it by 2:

431,405,039 ÷ 2 = 215,702,519.5

If the quotient is a whole number, then 2 and 215,702,519.5 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:

1 431,405,039
-1 -431,405,039

Now, we try dividing 431,405,039 by 3:

431,405,039 ÷ 3 = 143,801,679.6667

If the quotient is a whole number, then 3 and 143,801,679.6667 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:

1 431,405,039
-1 -431,405,039

Let's try dividing by 4:

431,405,039 ÷ 4 = 107,851,259.75

If the quotient is a whole number, then 4 and 107,851,259.75 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:

1 431,405,039
-1 431,405,039
Keep dividing by the next highest number until you cannot divide anymore.

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

113172212893,757114,8271,492,7511,952,05925,376,76733,185,003431,405,039
-1-13-17-221-289-3,757-114,827-1,492,751-1,952,059-25,376,767-33,185,003-431,405,039

More Examples

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