Q: What are the factor combinations of the number 520,355,209?

 A:
Positive:   1 x 52035520911 x 47305019109 x 4773901197 x 26413971199 x 4339912167 x 2401272203 x 23620321473 x 24233
Negative: -1 x -520355209-11 x -47305019-109 x -4773901-197 x -2641397-1199 x -433991-2167 x -240127-2203 x -236203-21473 x -24233


How do I find the factor combinations of the number 520,355,209?

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 520,355,209, 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.

1 520,355,209
-1 -520,355,209

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 520,355,209.

Example:
1 x 520,355,209 = 520,355,209
and
-1 x -520,355,209 = 520,355,209
Notice both answers equal 520,355,209

With that explanation out of the way, let's continue. Next, we take the number 520,355,209 and divide it by 2:

520,355,209 ÷ 2 = 260,177,604.5

If the quotient is a whole number, then 2 and 260,177,604.5 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:

1 520,355,209
-1 -520,355,209

Now, we try dividing 520,355,209 by 3:

520,355,209 ÷ 3 = 173,451,736.3333

If the quotient is a whole number, then 3 and 173,451,736.3333 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:

1 520,355,209
-1 -520,355,209

Let's try dividing by 4:

520,355,209 ÷ 4 = 130,088,802.25

If the quotient is a whole number, then 4 and 130,088,802.25 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:

1 520,355,209
-1 520,355,209
Keep dividing by the next highest number until you cannot divide anymore.

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

1111091971,1992,1672,20321,47324,233236,203240,127433,9912,641,3974,773,90147,305,019520,355,209
-1-11-109-197-1,199-2,167-2,203-21,473-24,233-236,203-240,127-433,991-2,641,397-4,773,901-47,305,019-520,355,209

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