Q: What are the factor combinations of the number 321,713,525?

 A:
Positive:   1 x 3217135255 x 643427057 x 4595907517 x 1892432525 x 1286854135 x 919181585 x 3784865119 x 2703475175 x 1838363425 x 756973595 x 5406952975 x 108139
Negative: -1 x -321713525-5 x -64342705-7 x -45959075-17 x -18924325-25 x -12868541-35 x -9191815-85 x -3784865-119 x -2703475-175 x -1838363-425 x -756973-595 x -540695-2975 x -108139


How do I find the factor combinations of the number 321,713,525?

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 321,713,525, 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.

1 321,713,525
-1 -321,713,525

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 321,713,525.

Example:
1 x 321,713,525 = 321,713,525
and
-1 x -321,713,525 = 321,713,525
Notice both answers equal 321,713,525

With that explanation out of the way, let's continue. Next, we take the number 321,713,525 and divide it by 2:

321,713,525 ÷ 2 = 160,856,762.5

If the quotient is a whole number, then 2 and 160,856,762.5 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:

1 321,713,525
-1 -321,713,525

Now, we try dividing 321,713,525 by 3:

321,713,525 ÷ 3 = 107,237,841.6667

If the quotient is a whole number, then 3 and 107,237,841.6667 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:

1 321,713,525
-1 -321,713,525

Let's try dividing by 4:

321,713,525 ÷ 4 = 80,428,381.25

If the quotient is a whole number, then 4 and 80,428,381.25 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:

1 321,713,525
-1 321,713,525
Keep dividing by the next highest number until you cannot divide anymore.

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

157172535851191754255952,975108,139540,695756,9731,838,3632,703,4753,784,8659,191,81512,868,54118,924,32545,959,07564,342,705321,713,525
-1-5-7-17-25-35-85-119-175-425-595-2,975-108,139-540,695-756,973-1,838,363-2,703,475-3,784,865-9,191,815-12,868,541-18,924,325-45,959,075-64,342,705-321,713,525

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