Q: What are the factor combinations of the number 120,705,541?

 A:
Positive:   1 x 12070554111 x 1097323123 x 524806747 x 2568203253 x 477097517 x 2334731081 x 11166110151 x 11891
Negative: -1 x -120705541-11 x -10973231-23 x -5248067-47 x -2568203-253 x -477097-517 x -233473-1081 x -111661-10151 x -11891


How do I find the factor combinations of the number 120,705,541?

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 120,705,541, 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.

1 120,705,541
-1 -120,705,541

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 120,705,541.

Example:
1 x 120,705,541 = 120,705,541
and
-1 x -120,705,541 = 120,705,541
Notice both answers equal 120,705,541

With that explanation out of the way, let's continue. Next, we take the number 120,705,541 and divide it by 2:

120,705,541 ÷ 2 = 60,352,770.5

If the quotient is a whole number, then 2 and 60,352,770.5 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:

1 120,705,541
-1 -120,705,541

Now, we try dividing 120,705,541 by 3:

120,705,541 ÷ 3 = 40,235,180.3333

If the quotient is a whole number, then 3 and 40,235,180.3333 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:

1 120,705,541
-1 -120,705,541

Let's try dividing by 4:

120,705,541 ÷ 4 = 30,176,385.25

If the quotient is a whole number, then 4 and 30,176,385.25 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:

1 120,705,541
-1 120,705,541
Keep dividing by the next highest number until you cannot divide anymore.

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

11123472535171,08110,15111,891111,661233,473477,0972,568,2035,248,06710,973,231120,705,541
-1-11-23-47-253-517-1,081-10,151-11,891-111,661-233,473-477,097-2,568,203-5,248,067-10,973,231-120,705,541

More Examples

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