Q: What are the factor combinations of the number 413,040,605?

 A:
Positive:   1 x 4130406055 x 82608121383 x 10784351915 x 215687
Negative: -1 x -413040605-5 x -82608121-383 x -1078435-1915 x -215687


How do I find the factor combinations of the number 413,040,605?

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 413,040,605, 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.

1 413,040,605
-1 -413,040,605

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 413,040,605.

Example:
1 x 413,040,605 = 413,040,605
and
-1 x -413,040,605 = 413,040,605
Notice both answers equal 413,040,605

With that explanation out of the way, let's continue. Next, we take the number 413,040,605 and divide it by 2:

413,040,605 ÷ 2 = 206,520,302.5

If the quotient is a whole number, then 2 and 206,520,302.5 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:

1 413,040,605
-1 -413,040,605

Now, we try dividing 413,040,605 by 3:

413,040,605 ÷ 3 = 137,680,201.6667

If the quotient is a whole number, then 3 and 137,680,201.6667 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:

1 413,040,605
-1 -413,040,605

Let's try dividing by 4:

413,040,605 ÷ 4 = 103,260,151.25

If the quotient is a whole number, then 4 and 103,260,151.25 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:

1 413,040,605
-1 413,040,605
Keep dividing by the next highest number until you cannot divide anymore.

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

153831,915215,6871,078,43582,608,121413,040,605
-1-5-383-1,915-215,687-1,078,435-82,608,121-413,040,605

More Examples

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