Q: What are the factor combinations of the number 109,585,223?

 A:
Positive:   1 x 10958522311 x 9962293121 x 905663281 x 389983293 x 3740111331 x 823333091 x 354533223 x 34001
Negative: -1 x -109585223-11 x -9962293-121 x -905663-281 x -389983-293 x -374011-1331 x -82333-3091 x -35453-3223 x -34001


How do I find the factor combinations of the number 109,585,223?

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 109,585,223, 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.

1 109,585,223
-1 -109,585,223

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 109,585,223.

Example:
1 x 109,585,223 = 109,585,223
and
-1 x -109,585,223 = 109,585,223
Notice both answers equal 109,585,223

With that explanation out of the way, let's continue. Next, we take the number 109,585,223 and divide it by 2:

109,585,223 ÷ 2 = 54,792,611.5

If the quotient is a whole number, then 2 and 54,792,611.5 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:

1 109,585,223
-1 -109,585,223

Now, we try dividing 109,585,223 by 3:

109,585,223 ÷ 3 = 36,528,407.6667

If the quotient is a whole number, then 3 and 36,528,407.6667 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:

1 109,585,223
-1 -109,585,223

Let's try dividing by 4:

109,585,223 ÷ 4 = 27,396,305.75

If the quotient is a whole number, then 4 and 27,396,305.75 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:

1 109,585,223
-1 109,585,223
Keep dividing by the next highest number until you cannot divide anymore.

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

1111212812931,3313,0913,22334,00135,45382,333374,011389,983905,6639,962,293109,585,223
-1-11-121-281-293-1,331-3,091-3,223-34,001-35,453-82,333-374,011-389,983-905,663-9,962,293-109,585,223

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