Q: What are the factor combinations of the number 120,405,187?

 A:
Positive:   1 x 1204051877 x 1720074129 x 4151903203 x 593129449 x 2681631321 x 911473143 x 383099247 x 13021
Negative: -1 x -120405187-7 x -17200741-29 x -4151903-203 x -593129-449 x -268163-1321 x -91147-3143 x -38309-9247 x -13021


How do I find the factor combinations of the number 120,405,187?

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 120,405,187, 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.

1 120,405,187
-1 -120,405,187

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 120,405,187.

Example:
1 x 120,405,187 = 120,405,187
and
-1 x -120,405,187 = 120,405,187
Notice both answers equal 120,405,187

With that explanation out of the way, let's continue. Next, we take the number 120,405,187 and divide it by 2:

120,405,187 ÷ 2 = 60,202,593.5

If the quotient is a whole number, then 2 and 60,202,593.5 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:

1 120,405,187
-1 -120,405,187

Now, we try dividing 120,405,187 by 3:

120,405,187 ÷ 3 = 40,135,062.3333

If the quotient is a whole number, then 3 and 40,135,062.3333 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:

1 120,405,187
-1 -120,405,187

Let's try dividing by 4:

120,405,187 ÷ 4 = 30,101,296.75

If the quotient is a whole number, then 4 and 30,101,296.75 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:

1 120,405,187
-1 120,405,187
Keep dividing by the next highest number until you cannot divide anymore.

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

17292034491,3213,1439,24713,02138,30991,147268,163593,1294,151,90317,200,741120,405,187
-1-7-29-203-449-1,321-3,143-9,247-13,021-38,309-91,147-268,163-593,129-4,151,903-17,200,741-120,405,187

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