Q: What are the factor combinations of the number 120,311,405?

 A:
Positive:   1 x 1203114055 x 2406228183 x 1449535239 x 503395415 x 2899071195 x 1006791213 x 991856065 x 19837
Negative: -1 x -120311405-5 x -24062281-83 x -1449535-239 x -503395-415 x -289907-1195 x -100679-1213 x -99185-6065 x -19837


How do I find the factor combinations of the number 120,311,405?

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 120,311,405, 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.

1 120,311,405
-1 -120,311,405

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 120,311,405.

Example:
1 x 120,311,405 = 120,311,405
and
-1 x -120,311,405 = 120,311,405
Notice both answers equal 120,311,405

With that explanation out of the way, let's continue. Next, we take the number 120,311,405 and divide it by 2:

120,311,405 ÷ 2 = 60,155,702.5

If the quotient is a whole number, then 2 and 60,155,702.5 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:

1 120,311,405
-1 -120,311,405

Now, we try dividing 120,311,405 by 3:

120,311,405 ÷ 3 = 40,103,801.6667

If the quotient is a whole number, then 3 and 40,103,801.6667 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:

1 120,311,405
-1 -120,311,405

Let's try dividing by 4:

120,311,405 ÷ 4 = 30,077,851.25

If the quotient is a whole number, then 4 and 30,077,851.25 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:

1 120,311,405
-1 120,311,405
Keep dividing by the next highest number until you cannot divide anymore.

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

15832394151,1951,2136,06519,83799,185100,679289,907503,3951,449,53524,062,281120,311,405
-1-5-83-239-415-1,195-1,213-6,065-19,837-99,185-100,679-289,907-503,395-1,449,535-24,062,281-120,311,405

More Examples

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