Q: What are the factor combinations of the number 123,023,431?

 A:
Positive:   1 x 123023431271 x 453961
Negative: -1 x -123023431-271 x -453961


How do I find the factor combinations of the number 123,023,431?

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 123,023,431, 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.

1 123,023,431
-1 -123,023,431

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 123,023,431.

Example:
1 x 123,023,431 = 123,023,431
and
-1 x -123,023,431 = 123,023,431
Notice both answers equal 123,023,431

With that explanation out of the way, let's continue. Next, we take the number 123,023,431 and divide it by 2:

123,023,431 ÷ 2 = 61,511,715.5

If the quotient is a whole number, then 2 and 61,511,715.5 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:

1 123,023,431
-1 -123,023,431

Now, we try dividing 123,023,431 by 3:

123,023,431 ÷ 3 = 41,007,810.3333

If the quotient is a whole number, then 3 and 41,007,810.3333 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:

1 123,023,431
-1 -123,023,431

Let's try dividing by 4:

123,023,431 ÷ 4 = 30,755,857.75

If the quotient is a whole number, then 4 and 30,755,857.75 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:

1 123,023,431
-1 123,023,431
Keep dividing by the next highest number until you cannot divide anymore.

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

1271453,961123,023,431
-1-271-453,961-123,023,431

More Examples

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