A:
Positive:
1 x 4141116777 x 5915881129 x 14279713149 x 2779273203 x 20399591043 x 3970394321 x 9583713691 x 30247
Negative:
-1 x -414111677-7 x -59158811-29 x -14279713-149 x -2779273-203 x -2039959-1043 x -397039-4321 x -95837-13691 x -30247
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 414,111,677, 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 | 414,111,677 | |
| -1 | -414,111,677 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 414,111,677.
Example:
1 x 414,111,677 = 414,111,677
and
-1 x -414,111,677 = 414,111,677
Notice both answers equal 414,111,677
With that explanation out of the way, let's continue. Next, we take the number 414,111,677 and divide it by 2:
414,111,677 ÷ 2 = 207,055,838.5
If the quotient is a whole number, then 2 and 207,055,838.5 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 | 414,111,677 | |
| -1 | -414,111,677 |
Now, we try dividing 414,111,677 by 3:
414,111,677 ÷ 3 = 138,037,225.6667
If the quotient is a whole number, then 3 and 138,037,225.6667 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 | 414,111,677 | |
| -1 | -414,111,677 |
Let's try dividing by 4:
414,111,677 ÷ 4 = 103,527,919.25
If the quotient is a whole number, then 4 and 103,527,919.25 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 | 414,111,677 | |
| -1 | 414,111,677 |
If you did it right, you will end up with this table:
| 1 | 7 | 29 | 149 | 203 | 1,043 | 4,321 | 13,691 | 30,247 | 95,837 | 397,039 | 2,039,959 | 2,779,273 | 14,279,713 | 59,158,811 | 414,111,677 |
| -1 | -7 | -29 | -149 | -203 | -1,043 | -4,321 | -13,691 | -30,247 | -95,837 | -397,039 | -2,039,959 | -2,779,273 | -14,279,713 | -59,158,811 | -414,111,677 |
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