Q: What are the factor combinations of the number 120,348,905?

 A:
Positive:   1 x 1203489055 x 2406978147 x 256061571 x 1695055235 x 512123355 x 3390113337 x 360657213 x 16685
Negative: -1 x -120348905-5 x -24069781-47 x -2560615-71 x -1695055-235 x -512123-355 x -339011-3337 x -36065-7213 x -16685


How do I find the factor combinations of the number 120,348,905?

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 120,348,905, 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.

1 120,348,905
-1 -120,348,905

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 120,348,905.

Example:
1 x 120,348,905 = 120,348,905
and
-1 x -120,348,905 = 120,348,905
Notice both answers equal 120,348,905

With that explanation out of the way, let's continue. Next, we take the number 120,348,905 and divide it by 2:

120,348,905 ÷ 2 = 60,174,452.5

If the quotient is a whole number, then 2 and 60,174,452.5 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:

1 120,348,905
-1 -120,348,905

Now, we try dividing 120,348,905 by 3:

120,348,905 ÷ 3 = 40,116,301.6667

If the quotient is a whole number, then 3 and 40,116,301.6667 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:

1 120,348,905
-1 -120,348,905

Let's try dividing by 4:

120,348,905 ÷ 4 = 30,087,226.25

If the quotient is a whole number, then 4 and 30,087,226.25 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:

1 120,348,905
-1 120,348,905
Keep dividing by the next highest number until you cannot divide anymore.

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

1547712353553,3377,21316,68536,065339,011512,1231,695,0552,560,61524,069,781120,348,905
-1-5-47-71-235-355-3,337-7,213-16,685-36,065-339,011-512,123-1,695,055-2,560,615-24,069,781-120,348,905

More Examples

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