Q: What are the factor combinations of the number 23,003,105?

 A:
Positive:   1 x 230031055 x 460062123 x 1000135115 x 200027317 x 72565631 x 364551585 x 145133155 x 7291
Negative: -1 x -23003105-5 x -4600621-23 x -1000135-115 x -200027-317 x -72565-631 x -36455-1585 x -14513-3155 x -7291


How do I find the factor combinations of the number 23,003,105?

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 23,003,105, 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 23,003,105
-1 -23,003,105

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 23,003,105.

Example:
1 x 23,003,105 = 23,003,105
and
-1 x -23,003,105 = 23,003,105
Notice both answers equal 23,003,105

With that explanation out of the way, let's continue. Next, we take the number 23,003,105 and divide it by 2:

23,003,105 ÷ 2 = 11,501,552.5

If the quotient is a whole number, then 2 and 11,501,552.5 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 23,003,105
-1 -23,003,105

Now, we try dividing 23,003,105 by 3:

23,003,105 ÷ 3 = 7,667,701.6667

If the quotient is a whole number, then 3 and 7,667,701.6667 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 23,003,105
-1 -23,003,105

Let's try dividing by 4:

23,003,105 ÷ 4 = 5,750,776.25

If the quotient is a whole number, then 4 and 5,750,776.25 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 23,003,105
-1 23,003,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15231153176311,5853,1557,29114,51336,45572,565200,0271,000,1354,600,62123,003,105
-1-5-23-115-317-631-1,585-3,155-7,291-14,513-36,455-72,565-200,027-1,000,135-4,600,621-23,003,105

More Examples

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