Q: What are the factor combinations of the number 631,823?

 A:
Positive:   1 x 63182329 x 21787
Negative: -1 x -631823-29 x -21787


How do I find the factor combinations of the number 631,823?

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 631,823, 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.

1 631,823
-1 -631,823

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 631,823.

Example:
1 x 631,823 = 631,823
and
-1 x -631,823 = 631,823
Notice both answers equal 631,823

With that explanation out of the way, let's continue. Next, we take the number 631,823 and divide it by 2:

631,823 ÷ 2 = 315,911.5

If the quotient is a whole number, then 2 and 315,911.5 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:

1 631,823
-1 -631,823

Now, we try dividing 631,823 by 3:

631,823 ÷ 3 = 210,607.6667

If the quotient is a whole number, then 3 and 210,607.6667 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:

1 631,823
-1 -631,823

Let's try dividing by 4:

631,823 ÷ 4 = 157,955.75

If the quotient is a whole number, then 4 and 157,955.75 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:

1 631,823
-1 631,823
Keep dividing by the next highest number until you cannot divide anymore.

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

12921,787631,823
-1-29-21,787-631,823

More Examples

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