Q: What are the factor combinations of the number 355,005,305?

 A:
Positive:   1 x 3550053055 x 7100106117 x 2088266585 x 4176533139 x 2553995695 x 5107992363 x 15023511815 x 30047
Negative: -1 x -355005305-5 x -71001061-17 x -20882665-85 x -4176533-139 x -2553995-695 x -510799-2363 x -150235-11815 x -30047


How do I find the factor combinations of the number 355,005,305?

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 355,005,305, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

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.

1 355,005,305
-1 -355,005,305

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 355,005,305.

Example:
1 x 355,005,305 = 355,005,305
and
-1 x -355,005,305 = 355,005,305
Notice both answers equal 355,005,305

With that explanation out of the way, let's continue. Next, we take the number 355,005,305 and divide it by 2:

355,005,305 ÷ 2 = 177,502,652.5

If the quotient is a whole number, then 2 and 177,502,652.5 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:

1 355,005,305
-1 -355,005,305

Now, we try dividing 355,005,305 by 3:

355,005,305 ÷ 3 = 118,335,101.6667

If the quotient is a whole number, then 3 and 118,335,101.6667 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:

1 355,005,305
-1 -355,005,305

Let's try dividing by 4:

355,005,305 ÷ 4 = 88,751,326.25

If the quotient is a whole number, then 4 and 88,751,326.25 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:

1 355,005,305
-1 355,005,305
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1517851396952,36311,81530,047150,235510,7992,553,9954,176,53320,882,66571,001,061355,005,305
-1-5-17-85-139-695-2,363-11,815-30,047-150,235-510,799-2,553,995-4,176,533-20,882,665-71,001,061-355,005,305

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