Q: What are the factor combinations of the number 321,133,025?

 A:
Positive:   1 x 3211330255 x 6422660525 x 1284532179 x 4064975277 x 1159325395 x 812995587 x 5470751385 x 2318651975 x 1625992935 x 1094156925 x 4637314675 x 21883
Negative: -1 x -321133025-5 x -64226605-25 x -12845321-79 x -4064975-277 x -1159325-395 x -812995-587 x -547075-1385 x -231865-1975 x -162599-2935 x -109415-6925 x -46373-14675 x -21883


How do I find the factor combinations of the number 321,133,025?

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 321,133,025, 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.

1 321,133,025
-1 -321,133,025

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 321,133,025.

Example:
1 x 321,133,025 = 321,133,025
and
-1 x -321,133,025 = 321,133,025
Notice both answers equal 321,133,025

With that explanation out of the way, let's continue. Next, we take the number 321,133,025 and divide it by 2:

321,133,025 ÷ 2 = 160,566,512.5

If the quotient is a whole number, then 2 and 160,566,512.5 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:

1 321,133,025
-1 -321,133,025

Now, we try dividing 321,133,025 by 3:

321,133,025 ÷ 3 = 107,044,341.6667

If the quotient is a whole number, then 3 and 107,044,341.6667 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:

1 321,133,025
-1 -321,133,025

Let's try dividing by 4:

321,133,025 ÷ 4 = 80,283,256.25

If the quotient is a whole number, then 4 and 80,283,256.25 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:

1 321,133,025
-1 321,133,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1525792773955871,3851,9752,9356,92514,67521,88346,373109,415162,599231,865547,075812,9951,159,3254,064,97512,845,32164,226,605321,133,025
-1-5-25-79-277-395-587-1,385-1,975-2,935-6,925-14,675-21,883-46,373-109,415-162,599-231,865-547,075-812,995-1,159,325-4,064,975-12,845,321-64,226,605-321,133,025

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