Q: What are the factor combinations of the number 812,539?

 A:
Positive:   1 x 8125397 x 11607713 x 6250391 x 8929
Negative: -1 x -812539-7 x -116077-13 x -62503-91 x -8929


How do I find the factor combinations of the number 812,539?

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 812,539, 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.

1 812,539
-1 -812,539

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 812,539.

Example:
1 x 812,539 = 812,539
and
-1 x -812,539 = 812,539
Notice both answers equal 812,539

With that explanation out of the way, let's continue. Next, we take the number 812,539 and divide it by 2:

812,539 ÷ 2 = 406,269.5

If the quotient is a whole number, then 2 and 406,269.5 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:

1 812,539
-1 -812,539

Now, we try dividing 812,539 by 3:

812,539 ÷ 3 = 270,846.3333

If the quotient is a whole number, then 3 and 270,846.3333 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:

1 812,539
-1 -812,539

Let's try dividing by 4:

812,539 ÷ 4 = 203,134.75

If the quotient is a whole number, then 4 and 203,134.75 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:

1 812,539
-1 812,539
Keep dividing by the next highest number until you cannot divide anymore.

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

1713918,92962,503116,077812,539
-1-7-13-91-8,929-62,503-116,077-812,539

More Examples

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