A:
Positive:
1 x 4140057122 x 2070028563 x 1380019044 x 1035014286 x 690009528 x 5175071412 x 3450047616 x 2587535724 x 1725023848 x 8625119
Negative:
-1 x -414005712-2 x -207002856-3 x -138001904-4 x -103501428-6 x -69000952-8 x -51750714-12 x -34500476-16 x -25875357-24 x -17250238-48 x -8625119
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 414,005,712, 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 | 414,005,712 | |
| -1 | -414,005,712 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 414,005,712.
Example:
1 x 414,005,712 = 414,005,712
and
-1 x -414,005,712 = 414,005,712
Notice both answers equal 414,005,712
With that explanation out of the way, let's continue. Next, we take the number 414,005,712 and divide it by 2:
414,005,712 ÷ 2 = 207,002,856
If the quotient is a whole number, then 2 and 207,002,856 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 207,002,856 | 414,005,712 | |
| -1 | -2 | -207,002,856 | -414,005,712 |
Now, we try dividing 414,005,712 by 3:
414,005,712 ÷ 3 = 138,001,904
If the quotient is a whole number, then 3 and 138,001,904 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 3 | 138,001,904 | 207,002,856 | 414,005,712 | |
| -1 | -2 | -3 | -138,001,904 | -207,002,856 | -414,005,712 |
Let's try dividing by 4:
414,005,712 ÷ 4 = 103,501,428
If the quotient is a whole number, then 4 and 103,501,428 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 3 | 4 | 103,501,428 | 138,001,904 | 207,002,856 | 414,005,712 | |
| -1 | -2 | -3 | -4 | -103,501,428 | -138,001,904 | -207,002,856 | 414,005,712 |
If you did it right, you will end up with this table:
| 1 | 2 | 3 | 4 | 6 | 8 | 12 | 16 | 24 | 48 | 8,625,119 | 17,250,238 | 25,875,357 | 34,500,476 | 51,750,714 | 69,000,952 | 103,501,428 | 138,001,904 | 207,002,856 | 414,005,712 |
| -1 | -2 | -3 | -4 | -6 | -8 | -12 | -16 | -24 | -48 | -8,625,119 | -17,250,238 | -25,875,357 | -34,500,476 | -51,750,714 | -69,000,952 | -103,501,428 | -138,001,904 | -207,002,856 | -414,005,712 |
Here are some more numbers to try:
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