Q: What are the factor combinations of the number 109,081,705?

 A:
Positive:   1 x 1090817055 x 21816341179 x 609395307 x 355315397 x 274765895 x 1218791535 x 710631985 x 54953
Negative: -1 x -109081705-5 x -21816341-179 x -609395-307 x -355315-397 x -274765-895 x -121879-1535 x -71063-1985 x -54953


How do I find the factor combinations of the number 109,081,705?

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 109,081,705, 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.

1 109,081,705
-1 -109,081,705

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 109,081,705.

Example:
1 x 109,081,705 = 109,081,705
and
-1 x -109,081,705 = 109,081,705
Notice both answers equal 109,081,705

With that explanation out of the way, let's continue. Next, we take the number 109,081,705 and divide it by 2:

109,081,705 ÷ 2 = 54,540,852.5

If the quotient is a whole number, then 2 and 54,540,852.5 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:

1 109,081,705
-1 -109,081,705

Now, we try dividing 109,081,705 by 3:

109,081,705 ÷ 3 = 36,360,568.3333

If the quotient is a whole number, then 3 and 36,360,568.3333 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:

1 109,081,705
-1 -109,081,705

Let's try dividing by 4:

109,081,705 ÷ 4 = 27,270,426.25

If the quotient is a whole number, then 4 and 27,270,426.25 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:

1 109,081,705
-1 109,081,705
Keep dividing by the next highest number until you cannot divide anymore.

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

151793073978951,5351,98554,95371,063121,879274,765355,315609,39521,816,341109,081,705
-1-5-179-307-397-895-1,535-1,985-54,953-71,063-121,879-274,765-355,315-609,395-21,816,341-109,081,705

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