Q: What are the factor combinations of the number 321,413,323?

 A:
Positive:   1 x 3214133237 x 4591618911 x 2921939377 x 41741991459 x 2202972861 x 11234310213 x 3147116049 x 20027
Negative: -1 x -321413323-7 x -45916189-11 x -29219393-77 x -4174199-1459 x -220297-2861 x -112343-10213 x -31471-16049 x -20027


How do I find the factor combinations of the number 321,413,323?

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 321,413,323, 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.

1 321,413,323
-1 -321,413,323

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 321,413,323.

Example:
1 x 321,413,323 = 321,413,323
and
-1 x -321,413,323 = 321,413,323
Notice both answers equal 321,413,323

With that explanation out of the way, let's continue. Next, we take the number 321,413,323 and divide it by 2:

321,413,323 ÷ 2 = 160,706,661.5

If the quotient is a whole number, then 2 and 160,706,661.5 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:

1 321,413,323
-1 -321,413,323

Now, we try dividing 321,413,323 by 3:

321,413,323 ÷ 3 = 107,137,774.3333

If the quotient is a whole number, then 3 and 107,137,774.3333 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:

1 321,413,323
-1 -321,413,323

Let's try dividing by 4:

321,413,323 ÷ 4 = 80,353,330.75

If the quotient is a whole number, then 4 and 80,353,330.75 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:

1 321,413,323
-1 321,413,323
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771,4592,86110,21316,04920,02731,471112,343220,2974,174,19929,219,39345,916,189321,413,323
-1-7-11-77-1,459-2,861-10,213-16,049-20,027-31,471-112,343-220,297-4,174,199-29,219,393-45,916,189-321,413,323

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