Q: What are the factor combinations of the number 516,404,125?

 A:
Positive:   1 x 5164041255 x 10328082525 x 20656165125 x 4131233937 x 5511254409 x 1171254685 x 11022522045 x 23425
Negative: -1 x -516404125-5 x -103280825-25 x -20656165-125 x -4131233-937 x -551125-4409 x -117125-4685 x -110225-22045 x -23425


How do I find the factor combinations of the number 516,404,125?

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 516,404,125, 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.

1 516,404,125
-1 -516,404,125

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 516,404,125.

Example:
1 x 516,404,125 = 516,404,125
and
-1 x -516,404,125 = 516,404,125
Notice both answers equal 516,404,125

With that explanation out of the way, let's continue. Next, we take the number 516,404,125 and divide it by 2:

516,404,125 ÷ 2 = 258,202,062.5

If the quotient is a whole number, then 2 and 258,202,062.5 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:

1 516,404,125
-1 -516,404,125

Now, we try dividing 516,404,125 by 3:

516,404,125 ÷ 3 = 172,134,708.3333

If the quotient is a whole number, then 3 and 172,134,708.3333 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:

1 516,404,125
-1 -516,404,125

Let's try dividing by 4:

516,404,125 ÷ 4 = 129,101,031.25

If the quotient is a whole number, then 4 and 129,101,031.25 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:

1 516,404,125
-1 516,404,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251259374,4094,68522,04523,425110,225117,125551,1254,131,23320,656,165103,280,825516,404,125
-1-5-25-125-937-4,409-4,685-22,045-23,425-110,225-117,125-551,125-4,131,233-20,656,165-103,280,825-516,404,125

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