Q: What are the factor combinations of the number 300,404,123?

 A:
Positive:   1 x 300404123263 x 1142221463 x 6488212467 x 121769
Negative: -1 x -300404123-263 x -1142221-463 x -648821-2467 x -121769


How do I find the factor combinations of the number 300,404,123?

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 300,404,123, 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.

1 300,404,123
-1 -300,404,123

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 300,404,123.

Example:
1 x 300,404,123 = 300,404,123
and
-1 x -300,404,123 = 300,404,123
Notice both answers equal 300,404,123

With that explanation out of the way, let's continue. Next, we take the number 300,404,123 and divide it by 2:

300,404,123 ÷ 2 = 150,202,061.5

If the quotient is a whole number, then 2 and 150,202,061.5 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:

1 300,404,123
-1 -300,404,123

Now, we try dividing 300,404,123 by 3:

300,404,123 ÷ 3 = 100,134,707.6667

If the quotient is a whole number, then 3 and 100,134,707.6667 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:

1 300,404,123
-1 -300,404,123

Let's try dividing by 4:

300,404,123 ÷ 4 = 75,101,030.75

If the quotient is a whole number, then 4 and 75,101,030.75 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:

1 300,404,123
-1 300,404,123
Keep dividing by the next highest number until you cannot divide anymore.

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

12634632,467121,769648,8211,142,221300,404,123
-1-263-463-2,467-121,769-648,821-1,142,221-300,404,123

More Examples

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