Q: What are the factor combinations of the number 120,322,405?

 A:
Positive:   1 x 1203224055 x 240644817 x 1718891535 x 3437783479 x 2511952395 x 502393353 x 358857177 x 16765
Negative: -1 x -120322405-5 x -24064481-7 x -17188915-35 x -3437783-479 x -251195-2395 x -50239-3353 x -35885-7177 x -16765


How do I find the factor combinations of the number 120,322,405?

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 120,322,405, 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.

1 120,322,405
-1 -120,322,405

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 120,322,405.

Example:
1 x 120,322,405 = 120,322,405
and
-1 x -120,322,405 = 120,322,405
Notice both answers equal 120,322,405

With that explanation out of the way, let's continue. Next, we take the number 120,322,405 and divide it by 2:

120,322,405 ÷ 2 = 60,161,202.5

If the quotient is a whole number, then 2 and 60,161,202.5 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:

1 120,322,405
-1 -120,322,405

Now, we try dividing 120,322,405 by 3:

120,322,405 ÷ 3 = 40,107,468.3333

If the quotient is a whole number, then 3 and 40,107,468.3333 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:

1 120,322,405
-1 -120,322,405

Let's try dividing by 4:

120,322,405 ÷ 4 = 30,080,601.25

If the quotient is a whole number, then 4 and 30,080,601.25 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:

1 120,322,405
-1 120,322,405
Keep dividing by the next highest number until you cannot divide anymore.

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

157354792,3953,3537,17716,76535,88550,239251,1953,437,78317,188,91524,064,481120,322,405
-1-5-7-35-479-2,395-3,353-7,177-16,765-35,885-50,239-251,195-3,437,783-17,188,915-24,064,481-120,322,405

More Examples

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