Q: What are the factor combinations of the number 320,411,441?

 A:
Positive:   1 x 3204114417 x 4577306349 x 6539009941 x 3405016587 x 486436949 x 46109
Negative: -1 x -320411441-7 x -45773063-49 x -6539009-941 x -340501-6587 x -48643-6949 x -46109


How do I find the factor combinations of the number 320,411,441?

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 320,411,441, 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.

1 320,411,441
-1 -320,411,441

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 320,411,441.

Example:
1 x 320,411,441 = 320,411,441
and
-1 x -320,411,441 = 320,411,441
Notice both answers equal 320,411,441

With that explanation out of the way, let's continue. Next, we take the number 320,411,441 and divide it by 2:

320,411,441 ÷ 2 = 160,205,720.5

If the quotient is a whole number, then 2 and 160,205,720.5 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:

1 320,411,441
-1 -320,411,441

Now, we try dividing 320,411,441 by 3:

320,411,441 ÷ 3 = 106,803,813.6667

If the quotient is a whole number, then 3 and 106,803,813.6667 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:

1 320,411,441
-1 -320,411,441

Let's try dividing by 4:

320,411,441 ÷ 4 = 80,102,860.25

If the quotient is a whole number, then 4 and 80,102,860.25 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:

1 320,411,441
-1 320,411,441
Keep dividing by the next highest number until you cannot divide anymore.

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

17499416,5876,94946,10948,643340,5016,539,00945,773,063320,411,441
-1-7-49-941-6,587-6,949-46,109-48,643-340,501-6,539,009-45,773,063-320,411,441

More Examples

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