Q: What are the factor combinations of the number 589,897?

 A:
Positive:   1 x 5898977 x 8427111 x 5362747 x 1255177 x 7661163 x 3619329 x 1793517 x 1141
Negative: -1 x -589897-7 x -84271-11 x -53627-47 x -12551-77 x -7661-163 x -3619-329 x -1793-517 x -1141


How do I find the factor combinations of the number 589,897?

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 589,897, 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.

1 589,897
-1 -589,897

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 589,897.

Example:
1 x 589,897 = 589,897
and
-1 x -589,897 = 589,897
Notice both answers equal 589,897

With that explanation out of the way, let's continue. Next, we take the number 589,897 and divide it by 2:

589,897 ÷ 2 = 294,948.5

If the quotient is a whole number, then 2 and 294,948.5 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:

1 589,897
-1 -589,897

Now, we try dividing 589,897 by 3:

589,897 ÷ 3 = 196,632.3333

If the quotient is a whole number, then 3 and 196,632.3333 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:

1 589,897
-1 -589,897

Let's try dividing by 4:

589,897 ÷ 4 = 147,474.25

If the quotient is a whole number, then 4 and 147,474.25 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:

1 589,897
-1 589,897
Keep dividing by the next highest number until you cannot divide anymore.

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

171147771633295171,1411,7933,6197,66112,55153,62784,271589,897
-1-7-11-47-77-163-329-517-1,141-1,793-3,619-7,661-12,551-53,627-84,271-589,897

More Examples

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