Q: What are the factor combinations of the number 110,705,905?

 A:
Positive:   1 x 1107059055 x 2214118129 x 3817445145 x 763489263 x 4209351315 x 841872903 x 381357627 x 14515
Negative: -1 x -110705905-5 x -22141181-29 x -3817445-145 x -763489-263 x -420935-1315 x -84187-2903 x -38135-7627 x -14515


How do I find the factor combinations of the number 110,705,905?

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 110,705,905, 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.

1 110,705,905
-1 -110,705,905

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 110,705,905.

Example:
1 x 110,705,905 = 110,705,905
and
-1 x -110,705,905 = 110,705,905
Notice both answers equal 110,705,905

With that explanation out of the way, let's continue. Next, we take the number 110,705,905 and divide it by 2:

110,705,905 ÷ 2 = 55,352,952.5

If the quotient is a whole number, then 2 and 55,352,952.5 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:

1 110,705,905
-1 -110,705,905

Now, we try dividing 110,705,905 by 3:

110,705,905 ÷ 3 = 36,901,968.3333

If the quotient is a whole number, then 3 and 36,901,968.3333 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:

1 110,705,905
-1 -110,705,905

Let's try dividing by 4:

110,705,905 ÷ 4 = 27,676,476.25

If the quotient is a whole number, then 4 and 27,676,476.25 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:

1 110,705,905
-1 110,705,905
Keep dividing by the next highest number until you cannot divide anymore.

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

15291452631,3152,9037,62714,51538,13584,187420,935763,4893,817,44522,141,181110,705,905
-1-5-29-145-263-1,315-2,903-7,627-14,515-38,135-84,187-420,935-763,489-3,817,445-22,141,181-110,705,905

More Examples

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