Q: What are the factor combinations of the number 104,251,105?

 A:
Positive:   1 x 1042511055 x 208502217 x 1489301535 x 2978603229 x 4552451145 x 910491603 x 650358015 x 13007
Negative: -1 x -104251105-5 x -20850221-7 x -14893015-35 x -2978603-229 x -455245-1145 x -91049-1603 x -65035-8015 x -13007


How do I find the factor combinations of the number 104,251,105?

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 104,251,105, 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.

1 104,251,105
-1 -104,251,105

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 104,251,105.

Example:
1 x 104,251,105 = 104,251,105
and
-1 x -104,251,105 = 104,251,105
Notice both answers equal 104,251,105

With that explanation out of the way, let's continue. Next, we take the number 104,251,105 and divide it by 2:

104,251,105 ÷ 2 = 52,125,552.5

If the quotient is a whole number, then 2 and 52,125,552.5 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:

1 104,251,105
-1 -104,251,105

Now, we try dividing 104,251,105 by 3:

104,251,105 ÷ 3 = 34,750,368.3333

If the quotient is a whole number, then 3 and 34,750,368.3333 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:

1 104,251,105
-1 -104,251,105

Let's try dividing by 4:

104,251,105 ÷ 4 = 26,062,776.25

If the quotient is a whole number, then 4 and 26,062,776.25 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:

1 104,251,105
-1 104,251,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157352291,1451,6038,01513,00765,03591,049455,2452,978,60314,893,01520,850,221104,251,105
-1-5-7-35-229-1,145-1,603-8,015-13,007-65,035-91,049-455,245-2,978,603-14,893,015-20,850,221-104,251,105

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