Q: What are the factor combinations of the number 361,263,305?

 A:
Positive:   1 x 3612633055 x 7225266113 x 2778948531 x 1165365565 x 5557897155 x 2330731403 x 8964352015 x 179287
Negative: -1 x -361263305-5 x -72252661-13 x -27789485-31 x -11653655-65 x -5557897-155 x -2330731-403 x -896435-2015 x -179287


How do I find the factor combinations of the number 361,263,305?

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 361,263,305, 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.

1 361,263,305
-1 -361,263,305

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 361,263,305.

Example:
1 x 361,263,305 = 361,263,305
and
-1 x -361,263,305 = 361,263,305
Notice both answers equal 361,263,305

With that explanation out of the way, let's continue. Next, we take the number 361,263,305 and divide it by 2:

361,263,305 ÷ 2 = 180,631,652.5

If the quotient is a whole number, then 2 and 180,631,652.5 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:

1 361,263,305
-1 -361,263,305

Now, we try dividing 361,263,305 by 3:

361,263,305 ÷ 3 = 120,421,101.6667

If the quotient is a whole number, then 3 and 120,421,101.6667 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:

1 361,263,305
-1 -361,263,305

Let's try dividing by 4:

361,263,305 ÷ 4 = 90,315,826.25

If the quotient is a whole number, then 4 and 90,315,826.25 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:

1 361,263,305
-1 361,263,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151331651554032,015179,287896,4352,330,7315,557,89711,653,65527,789,48572,252,661361,263,305
-1-5-13-31-65-155-403-2,015-179,287-896,435-2,330,731-5,557,897-11,653,655-27,789,485-72,252,661-361,263,305

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