Q: What are the factor combinations of the number 392,639?

 A:
Positive:   1 x 39263913 x 30203
Negative: -1 x -392639-13 x -30203


How do I find the factor combinations of the number 392,639?

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 392,639, 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.

1 392,639
-1 -392,639

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 392,639.

Example:
1 x 392,639 = 392,639
and
-1 x -392,639 = 392,639
Notice both answers equal 392,639

With that explanation out of the way, let's continue. Next, we take the number 392,639 and divide it by 2:

392,639 ÷ 2 = 196,319.5

If the quotient is a whole number, then 2 and 196,319.5 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:

1 392,639
-1 -392,639

Now, we try dividing 392,639 by 3:

392,639 ÷ 3 = 130,879.6667

If the quotient is a whole number, then 3 and 130,879.6667 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:

1 392,639
-1 -392,639

Let's try dividing by 4:

392,639 ÷ 4 = 98,159.75

If the quotient is a whole number, then 4 and 98,159.75 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:

1 392,639
-1 392,639
Keep dividing by the next highest number until you cannot divide anymore.

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

11330,203392,639
-1-13-30,203-392,639

More Examples

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