A:
Positive:
1 x 2113150255 x 4226300525 x 845260129 x 728672541 x 5154025145 x 1457345205 x 1030805725 x 2914691025 x 2061611189 x 1777255945 x 355457109 x 29725
Negative:
-1 x -211315025-5 x -42263005-25 x -8452601-29 x -7286725-41 x -5154025-145 x -1457345-205 x -1030805-725 x -291469-1025 x -206161-1189 x -177725-5945 x -35545-7109 x -29725
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 211,315,025, 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 | 211,315,025 | |
| -1 | -211,315,025 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 211,315,025.
Example:
1 x 211,315,025 = 211,315,025
and
-1 x -211,315,025 = 211,315,025
Notice both answers equal 211,315,025
With that explanation out of the way, let's continue. Next, we take the number 211,315,025 and divide it by 2:
211,315,025 ÷ 2 = 105,657,512.5
If the quotient is a whole number, then 2 and 105,657,512.5 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 | 211,315,025 | |
| -1 | -211,315,025 |
Now, we try dividing 211,315,025 by 3:
211,315,025 ÷ 3 = 70,438,341.6667
If the quotient is a whole number, then 3 and 70,438,341.6667 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 | 211,315,025 | |
| -1 | -211,315,025 |
Let's try dividing by 4:
211,315,025 ÷ 4 = 52,828,756.25
If the quotient is a whole number, then 4 and 52,828,756.25 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 | 211,315,025 | |
| -1 | 211,315,025 |
If you did it right, you will end up with this table:
| 1 | 5 | 25 | 29 | 41 | 145 | 205 | 725 | 1,025 | 1,189 | 5,945 | 7,109 | 29,725 | 35,545 | 177,725 | 206,161 | 291,469 | 1,030,805 | 1,457,345 | 5,154,025 | 7,286,725 | 8,452,601 | 42,263,005 | 211,315,025 |
| -1 | -5 | -25 | -29 | -41 | -145 | -205 | -725 | -1,025 | -1,189 | -5,945 | -7,109 | -29,725 | -35,545 | -177,725 | -206,161 | -291,469 | -1,030,805 | -1,457,345 | -5,154,025 | -7,286,725 | -8,452,601 | -42,263,005 | -211,315,025 |
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