Q: What are the factor combinations of the number 124,000,413?

 A:
Positive:   1 x 1240004133 x 41333471
Negative: -1 x -124000413-3 x -41333471


How do I find the factor combinations of the number 124,000,413?

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 124,000,413, 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.

1 124,000,413
-1 -124,000,413

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 124,000,413.

Example:
1 x 124,000,413 = 124,000,413
and
-1 x -124,000,413 = 124,000,413
Notice both answers equal 124,000,413

With that explanation out of the way, let's continue. Next, we take the number 124,000,413 and divide it by 2:

124,000,413 ÷ 2 = 62,000,206.5

If the quotient is a whole number, then 2 and 62,000,206.5 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:

1 124,000,413
-1 -124,000,413

Now, we try dividing 124,000,413 by 3:

124,000,413 ÷ 3 = 41,333,471

If the quotient is a whole number, then 3 and 41,333,471 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 41,333,471 124,000,413
-1 -3 -41,333,471 -124,000,413

Let's try dividing by 4:

124,000,413 ÷ 4 = 31,000,103.25

If the quotient is a whole number, then 4 and 31,000,103.25 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 3 41,333,471 124,000,413
-1 -3 -41,333,471 124,000,413
Keep dividing by the next highest number until you cannot divide anymore.

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

1341,333,471124,000,413
-1-3-41,333,471-124,000,413

More Examples

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