A:
Positive:
1 x 2130041277 x 3042916123 x 926104949 x 4347023161 x 1323007331 x 643517571 x 3730371127 x 1890012317 x 919313997 x 532917613 x 2797913133 x 16219
Negative:
-1 x -213004127-7 x -30429161-23 x -9261049-49 x -4347023-161 x -1323007-331 x -643517-571 x -373037-1127 x -189001-2317 x -91931-3997 x -53291-7613 x -27979-13133 x -16219
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 213,004,127, it is easier to work with a table - it's called factoring from the outside in.
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 | 213,004,127 | |
| -1 | -213,004,127 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 213,004,127.
Example:
1 x 213,004,127 = 213,004,127
and
-1 x -213,004,127 = 213,004,127
Notice both answers equal 213,004,127
With that explanation out of the way, let's continue. Next, we take the number 213,004,127 and divide it by 2:
213,004,127 ÷ 2 = 106,502,063.5
If the quotient is a whole number, then 2 and 106,502,063.5 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 | 213,004,127 | |
| -1 | -213,004,127 |
Now, we try dividing 213,004,127 by 3:
213,004,127 ÷ 3 = 71,001,375.6667
If the quotient is a whole number, then 3 and 71,001,375.6667 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 | 213,004,127 | |
| -1 | -213,004,127 |
Let's try dividing by 4:
213,004,127 ÷ 4 = 53,251,031.75
If the quotient is a whole number, then 4 and 53,251,031.75 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 | 213,004,127 | |
| -1 | 213,004,127 |
If you did it right, you will end up with this table:
| 1 | 7 | 23 | 49 | 161 | 331 | 571 | 1,127 | 2,317 | 3,997 | 7,613 | 13,133 | 16,219 | 27,979 | 53,291 | 91,931 | 189,001 | 373,037 | 643,517 | 1,323,007 | 4,347,023 | 9,261,049 | 30,429,161 | 213,004,127 |
| -1 | -7 | -23 | -49 | -161 | -331 | -571 | -1,127 | -2,317 | -3,997 | -7,613 | -13,133 | -16,219 | -27,979 | -53,291 | -91,931 | -189,001 | -373,037 | -643,517 | -1,323,007 | -4,347,023 | -9,261,049 | -30,429,161 | -213,004,127 |
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