Q: What are the factor combinations of the number 205,789?

 A:
Positive:   1 x 20578919 x 10831
Negative: -1 x -205789-19 x -10831


How do I find the factor combinations of the number 205,789?

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 205,789, 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.

1 205,789
-1 -205,789

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 205,789.

Example:
1 x 205,789 = 205,789
and
-1 x -205,789 = 205,789
Notice both answers equal 205,789

With that explanation out of the way, let's continue. Next, we take the number 205,789 and divide it by 2:

205,789 ÷ 2 = 102,894.5

If the quotient is a whole number, then 2 and 102,894.5 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:

1 205,789
-1 -205,789

Now, we try dividing 205,789 by 3:

205,789 ÷ 3 = 68,596.3333

If the quotient is a whole number, then 3 and 68,596.3333 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:

1 205,789
-1 -205,789

Let's try dividing by 4:

205,789 ÷ 4 = 51,447.25

If the quotient is a whole number, then 4 and 51,447.25 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:

1 205,789
-1 205,789
Keep dividing by the next highest number until you cannot divide anymore.

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

11910,831205,789
-1-19-10,831-205,789

More Examples

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