A:
Positive:
1 x 4142223055 x 828444617 x 5917461535 x 11834923811 x 5107554055 x 1021515677 x 7296514593 x 28385
Negative:
-1 x -414222305-5 x -82844461-7 x -59174615-35 x -11834923-811 x -510755-4055 x -102151-5677 x -72965-14593 x -28385
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 414,222,305, 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 | 414,222,305 | |
| -1 | -414,222,305 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 414,222,305.
Example:
1 x 414,222,305 = 414,222,305
and
-1 x -414,222,305 = 414,222,305
Notice both answers equal 414,222,305
With that explanation out of the way, let's continue. Next, we take the number 414,222,305 and divide it by 2:
414,222,305 ÷ 2 = 207,111,152.5
If the quotient is a whole number, then 2 and 207,111,152.5 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 | 414,222,305 | |
| -1 | -414,222,305 |
Now, we try dividing 414,222,305 by 3:
414,222,305 ÷ 3 = 138,074,101.6667
If the quotient is a whole number, then 3 and 138,074,101.6667 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 | 414,222,305 | |
| -1 | -414,222,305 |
Let's try dividing by 4:
414,222,305 ÷ 4 = 103,555,576.25
If the quotient is a whole number, then 4 and 103,555,576.25 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 | 414,222,305 | |
| -1 | 414,222,305 |
If you did it right, you will end up with this table:
| 1 | 5 | 7 | 35 | 811 | 4,055 | 5,677 | 14,593 | 28,385 | 72,965 | 102,151 | 510,755 | 11,834,923 | 59,174,615 | 82,844,461 | 414,222,305 |
| -1 | -5 | -7 | -35 | -811 | -4,055 | -5,677 | -14,593 | -28,385 | -72,965 | -102,151 | -510,755 | -11,834,923 | -59,174,615 | -82,844,461 | -414,222,305 |
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