Q: What are the factor combinations of the number 521,320,129?

 A:
Positive:   1 x 52132012911 x 47392739163 x 3198283479 x 1088351607 x 8588471793 x 2907535269 x 989416677 x 78077
Negative: -1 x -521320129-11 x -47392739-163 x -3198283-479 x -1088351-607 x -858847-1793 x -290753-5269 x -98941-6677 x -78077


How do I find the factor combinations of the number 521,320,129?

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 521,320,129, 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.

1 521,320,129
-1 -521,320,129

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 521,320,129.

Example:
1 x 521,320,129 = 521,320,129
and
-1 x -521,320,129 = 521,320,129
Notice both answers equal 521,320,129

With that explanation out of the way, let's continue. Next, we take the number 521,320,129 and divide it by 2:

521,320,129 ÷ 2 = 260,660,064.5

If the quotient is a whole number, then 2 and 260,660,064.5 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:

1 521,320,129
-1 -521,320,129

Now, we try dividing 521,320,129 by 3:

521,320,129 ÷ 3 = 173,773,376.3333

If the quotient is a whole number, then 3 and 173,773,376.3333 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:

1 521,320,129
-1 -521,320,129

Let's try dividing by 4:

521,320,129 ÷ 4 = 130,330,032.25

If the quotient is a whole number, then 4 and 130,330,032.25 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:

1 521,320,129
-1 521,320,129
Keep dividing by the next highest number until you cannot divide anymore.

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

1111634796071,7935,2696,67778,07798,941290,753858,8471,088,3513,198,28347,392,739521,320,129
-1-11-163-479-607-1,793-5,269-6,677-78,077-98,941-290,753-858,847-1,088,351-3,198,283-47,392,739-521,320,129

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