Q: What are the factor combinations of the number 523,124,315?

 A:
Positive:   1 x 5231243155 x 1046248637 x 7473204535 x 1494640937 x 14138495185 x 2827699259 x 20197851295 x 403957
Negative: -1 x -523124315-5 x -104624863-7 x -74732045-35 x -14946409-37 x -14138495-185 x -2827699-259 x -2019785-1295 x -403957


How do I find the factor combinations of the number 523,124,315?

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 523,124,315, 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.

1 523,124,315
-1 -523,124,315

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 523,124,315.

Example:
1 x 523,124,315 = 523,124,315
and
-1 x -523,124,315 = 523,124,315
Notice both answers equal 523,124,315

With that explanation out of the way, let's continue. Next, we take the number 523,124,315 and divide it by 2:

523,124,315 ÷ 2 = 261,562,157.5

If the quotient is a whole number, then 2 and 261,562,157.5 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:

1 523,124,315
-1 -523,124,315

Now, we try dividing 523,124,315 by 3:

523,124,315 ÷ 3 = 174,374,771.6667

If the quotient is a whole number, then 3 and 174,374,771.6667 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:

1 523,124,315
-1 -523,124,315

Let's try dividing by 4:

523,124,315 ÷ 4 = 130,781,078.75

If the quotient is a whole number, then 4 and 130,781,078.75 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:

1 523,124,315
-1 523,124,315
Keep dividing by the next highest number until you cannot divide anymore.

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

15735371852591,295403,9572,019,7852,827,69914,138,49514,946,40974,732,045104,624,863523,124,315
-1-5-7-35-37-185-259-1,295-403,957-2,019,785-2,827,699-14,138,495-14,946,409-74,732,045-104,624,863-523,124,315

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