Q: What are the factor combinations of the number 205,565,021?

 A:
Positive:   1 x 20556502129 x 708844941 x 501378183 x 24766871189 x 1728892083 x 986872407 x 854033403 x 60407
Negative: -1 x -205565021-29 x -7088449-41 x -5013781-83 x -2476687-1189 x -172889-2083 x -98687-2407 x -85403-3403 x -60407


How do I find the factor combinations of the number 205,565,021?

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 205,565,021, 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.

1 205,565,021
-1 -205,565,021

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 205,565,021.

Example:
1 x 205,565,021 = 205,565,021
and
-1 x -205,565,021 = 205,565,021
Notice both answers equal 205,565,021

With that explanation out of the way, let's continue. Next, we take the number 205,565,021 and divide it by 2:

205,565,021 ÷ 2 = 102,782,510.5

If the quotient is a whole number, then 2 and 102,782,510.5 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:

1 205,565,021
-1 -205,565,021

Now, we try dividing 205,565,021 by 3:

205,565,021 ÷ 3 = 68,521,673.6667

If the quotient is a whole number, then 3 and 68,521,673.6667 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:

1 205,565,021
-1 -205,565,021

Let's try dividing by 4:

205,565,021 ÷ 4 = 51,391,255.25

If the quotient is a whole number, then 4 and 51,391,255.25 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:

1 205,565,021
-1 205,565,021
Keep dividing by the next highest number until you cannot divide anymore.

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

12941831,1892,0832,4073,40360,40785,40398,687172,8892,476,6875,013,7817,088,449205,565,021
-1-29-41-83-1,189-2,083-2,407-3,403-60,407-85,403-98,687-172,889-2,476,687-5,013,781-7,088,449-205,565,021

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