Q: What are the factor combinations of the number 120,891,913?

 A:
Positive:   1 x 12089191317 x 711128937 x 326734971 x 1702703629 x 1921971207 x 1001592627 x 460192707 x 44659
Negative: -1 x -120891913-17 x -7111289-37 x -3267349-71 x -1702703-629 x -192197-1207 x -100159-2627 x -46019-2707 x -44659


How do I find the factor combinations of the number 120,891,913?

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 120,891,913, 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.

1 120,891,913
-1 -120,891,913

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 120,891,913.

Example:
1 x 120,891,913 = 120,891,913
and
-1 x -120,891,913 = 120,891,913
Notice both answers equal 120,891,913

With that explanation out of the way, let's continue. Next, we take the number 120,891,913 and divide it by 2:

120,891,913 ÷ 2 = 60,445,956.5

If the quotient is a whole number, then 2 and 60,445,956.5 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:

1 120,891,913
-1 -120,891,913

Now, we try dividing 120,891,913 by 3:

120,891,913 ÷ 3 = 40,297,304.3333

If the quotient is a whole number, then 3 and 40,297,304.3333 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:

1 120,891,913
-1 -120,891,913

Let's try dividing by 4:

120,891,913 ÷ 4 = 30,222,978.25

If the quotient is a whole number, then 4 and 30,222,978.25 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:

1 120,891,913
-1 120,891,913
Keep dividing by the next highest number until you cannot divide anymore.

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

11737716291,2072,6272,70744,65946,019100,159192,1971,702,7033,267,3497,111,289120,891,913
-1-17-37-71-629-1,207-2,627-2,707-44,659-46,019-100,159-192,197-1,702,703-3,267,349-7,111,289-120,891,913

More Examples

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