Q: What are the factor combinations of the number 360,311,605?

 A:
Positive:   1 x 3603116055 x 7206232131 x 1162295589 x 4048445155 x 2324591445 x 8096892759 x 13059513795 x 26119
Negative: -1 x -360311605-5 x -72062321-31 x -11622955-89 x -4048445-155 x -2324591-445 x -809689-2759 x -130595-13795 x -26119


How do I find the factor combinations of the number 360,311,605?

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 360,311,605, 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.

1 360,311,605
-1 -360,311,605

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 360,311,605.

Example:
1 x 360,311,605 = 360,311,605
and
-1 x -360,311,605 = 360,311,605
Notice both answers equal 360,311,605

With that explanation out of the way, let's continue. Next, we take the number 360,311,605 and divide it by 2:

360,311,605 ÷ 2 = 180,155,802.5

If the quotient is a whole number, then 2 and 180,155,802.5 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:

1 360,311,605
-1 -360,311,605

Now, we try dividing 360,311,605 by 3:

360,311,605 ÷ 3 = 120,103,868.3333

If the quotient is a whole number, then 3 and 120,103,868.3333 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:

1 360,311,605
-1 -360,311,605

Let's try dividing by 4:

360,311,605 ÷ 4 = 90,077,901.25

If the quotient is a whole number, then 4 and 90,077,901.25 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:

1 360,311,605
-1 360,311,605
Keep dividing by the next highest number until you cannot divide anymore.

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

1531891554452,75913,79526,119130,595809,6892,324,5914,048,44511,622,95572,062,321360,311,605
-1-5-31-89-155-445-2,759-13,795-26,119-130,595-809,689-2,324,591-4,048,445-11,622,955-72,062,321-360,311,605

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