Q: What are the factor combinations of the number 827,365?

 A:
Positive:   1 x 8273655 x 1654737 x 11819511 x 7521535 x 2363949 x 1688555 x 1504377 x 10745245 x 3377307 x 2695385 x 2149539 x 1535
Negative: -1 x -827365-5 x -165473-7 x -118195-11 x -75215-35 x -23639-49 x -16885-55 x -15043-77 x -10745-245 x -3377-307 x -2695-385 x -2149-539 x -1535


How do I find the factor combinations of the number 827,365?

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 827,365, 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.

1 827,365
-1 -827,365

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 827,365.

Example:
1 x 827,365 = 827,365
and
-1 x -827,365 = 827,365
Notice both answers equal 827,365

With that explanation out of the way, let's continue. Next, we take the number 827,365 and divide it by 2:

827,365 ÷ 2 = 413,682.5

If the quotient is a whole number, then 2 and 413,682.5 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:

1 827,365
-1 -827,365

Now, we try dividing 827,365 by 3:

827,365 ÷ 3 = 275,788.3333

If the quotient is a whole number, then 3 and 275,788.3333 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:

1 827,365
-1 -827,365

Let's try dividing by 4:

827,365 ÷ 4 = 206,841.25

If the quotient is a whole number, then 4 and 206,841.25 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:

1 827,365
-1 827,365
Keep dividing by the next highest number until you cannot divide anymore.

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

15711354955772453073855391,5352,1492,6953,37710,74515,04316,88523,63975,215118,195165,473827,365
-1-5-7-11-35-49-55-77-245-307-385-539-1,535-2,149-2,695-3,377-10,745-15,043-16,885-23,639-75,215-118,195-165,473-827,365

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