Q: What are the factor combinations of the number 120,111,305?

 A:
Positive:   1 x 1201113055 x 24022261173 x 694285191 x 628855727 x 165215865 x 138857955 x 1257713635 x 33043
Negative: -1 x -120111305-5 x -24022261-173 x -694285-191 x -628855-727 x -165215-865 x -138857-955 x -125771-3635 x -33043


How do I find the factor combinations of the number 120,111,305?

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 120,111,305, 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.

1 120,111,305
-1 -120,111,305

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 120,111,305.

Example:
1 x 120,111,305 = 120,111,305
and
-1 x -120,111,305 = 120,111,305
Notice both answers equal 120,111,305

With that explanation out of the way, let's continue. Next, we take the number 120,111,305 and divide it by 2:

120,111,305 ÷ 2 = 60,055,652.5

If the quotient is a whole number, then 2 and 60,055,652.5 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:

1 120,111,305
-1 -120,111,305

Now, we try dividing 120,111,305 by 3:

120,111,305 ÷ 3 = 40,037,101.6667

If the quotient is a whole number, then 3 and 40,037,101.6667 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:

1 120,111,305
-1 -120,111,305

Let's try dividing by 4:

120,111,305 ÷ 4 = 30,027,826.25

If the quotient is a whole number, then 4 and 30,027,826.25 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:

1 120,111,305
-1 120,111,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151731917278659553,63533,043125,771138,857165,215628,855694,28524,022,261120,111,305
-1-5-173-191-727-865-955-3,635-33,043-125,771-138,857-165,215-628,855-694,285-24,022,261-120,111,305

More Examples

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