Q: What are the factor combinations of the number 23,008,447?

 A:
Positive:   1 x 230084477 x 328692111 x 209167777 x 298811131 x 175637917 x 250911441 x 159672281 x 10087
Negative: -1 x -23008447-7 x -3286921-11 x -2091677-77 x -298811-131 x -175637-917 x -25091-1441 x -15967-2281 x -10087


How do I find the factor combinations of the number 23,008,447?

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 23,008,447, 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 23,008,447
-1 -23,008,447

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 23,008,447.

Example:
1 x 23,008,447 = 23,008,447
and
-1 x -23,008,447 = 23,008,447
Notice both answers equal 23,008,447

With that explanation out of the way, let's continue. Next, we take the number 23,008,447 and divide it by 2:

23,008,447 ÷ 2 = 11,504,223.5

If the quotient is a whole number, then 2 and 11,504,223.5 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 23,008,447
-1 -23,008,447

Now, we try dividing 23,008,447 by 3:

23,008,447 ÷ 3 = 7,669,482.3333

If the quotient is a whole number, then 3 and 7,669,482.3333 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 23,008,447
-1 -23,008,447

Let's try dividing by 4:

23,008,447 ÷ 4 = 5,752,111.75

If the quotient is a whole number, then 4 and 5,752,111.75 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 23,008,447
-1 23,008,447
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771319171,4412,28110,08715,96725,091175,637298,8112,091,6773,286,92123,008,447
-1-7-11-77-131-917-1,441-2,281-10,087-15,967-25,091-175,637-298,811-2,091,677-3,286,921-23,008,447

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