Q: What are the factor combinations of the number 24,213,305?

 A:
Positive:   1 x 242133055 x 484266159 x 410395211 x 114755295 x 82079389 x 622451055 x 229511945 x 12449
Negative: -1 x -24213305-5 x -4842661-59 x -410395-211 x -114755-295 x -82079-389 x -62245-1055 x -22951-1945 x -12449


How do I find the factor combinations of the number 24,213,305?

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 24,213,305, 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 24,213,305
-1 -24,213,305

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 24,213,305.

Example:
1 x 24,213,305 = 24,213,305
and
-1 x -24,213,305 = 24,213,305
Notice both answers equal 24,213,305

With that explanation out of the way, let's continue. Next, we take the number 24,213,305 and divide it by 2:

24,213,305 ÷ 2 = 12,106,652.5

If the quotient is a whole number, then 2 and 12,106,652.5 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 24,213,305
-1 -24,213,305

Now, we try dividing 24,213,305 by 3:

24,213,305 ÷ 3 = 8,071,101.6667

If the quotient is a whole number, then 3 and 8,071,101.6667 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 24,213,305
-1 -24,213,305

Let's try dividing by 4:

24,213,305 ÷ 4 = 6,053,326.25

If the quotient is a whole number, then 4 and 6,053,326.25 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 24,213,305
-1 24,213,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15592112953891,0551,94512,44922,95162,24582,079114,755410,3954,842,66124,213,305
-1-5-59-211-295-389-1,055-1,945-12,449-22,951-62,245-82,079-114,755-410,395-4,842,661-24,213,305

More Examples

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