Q: What are the factor combinations of the number 123,343?

 A:
Positive:   1 x 12334311 x 11213
Negative: -1 x -123343-11 x -11213


How do I find the factor combinations of the number 123,343?

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 123,343, 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.

1 123,343
-1 -123,343

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 123,343.

Example:
1 x 123,343 = 123,343
and
-1 x -123,343 = 123,343
Notice both answers equal 123,343

With that explanation out of the way, let's continue. Next, we take the number 123,343 and divide it by 2:

123,343 ÷ 2 = 61,671.5

If the quotient is a whole number, then 2 and 61,671.5 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:

1 123,343
-1 -123,343

Now, we try dividing 123,343 by 3:

123,343 ÷ 3 = 41,114.3333

If the quotient is a whole number, then 3 and 41,114.3333 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:

1 123,343
-1 -123,343

Let's try dividing by 4:

123,343 ÷ 4 = 30,835.75

If the quotient is a whole number, then 4 and 30,835.75 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:

1 123,343
-1 123,343
Keep dividing by the next highest number until you cannot divide anymore.

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

11111,213123,343
-1-11-11,213-123,343

More Examples

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