Q: What are the factor combinations of the number 109,007,665?

 A:
Positive:   1 x 1090076655 x 2180153313 x 838520529 x 375888565 x 1677041145 x 751777377 x 2891451885 x 57829
Negative: -1 x -109007665-5 x -21801533-13 x -8385205-29 x -3758885-65 x -1677041-145 x -751777-377 x -289145-1885 x -57829


How do I find the factor combinations of the number 109,007,665?

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 109,007,665, 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.

1 109,007,665
-1 -109,007,665

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 109,007,665.

Example:
1 x 109,007,665 = 109,007,665
and
-1 x -109,007,665 = 109,007,665
Notice both answers equal 109,007,665

With that explanation out of the way, let's continue. Next, we take the number 109,007,665 and divide it by 2:

109,007,665 ÷ 2 = 54,503,832.5

If the quotient is a whole number, then 2 and 54,503,832.5 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:

1 109,007,665
-1 -109,007,665

Now, we try dividing 109,007,665 by 3:

109,007,665 ÷ 3 = 36,335,888.3333

If the quotient is a whole number, then 3 and 36,335,888.3333 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:

1 109,007,665
-1 -109,007,665

Let's try dividing by 4:

109,007,665 ÷ 4 = 27,251,916.25

If the quotient is a whole number, then 4 and 27,251,916.25 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:

1 109,007,665
-1 109,007,665
Keep dividing by the next highest number until you cannot divide anymore.

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

151329651453771,88557,829289,145751,7771,677,0413,758,8858,385,20521,801,533109,007,665
-1-5-13-29-65-145-377-1,885-57,829-289,145-751,777-1,677,041-3,758,885-8,385,205-21,801,533-109,007,665

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