Q: What are the factor combinations of the number 21,424,105?

 A:
Positive:   1 x 214241055 x 428482143 x 498235215 x 99647251 x 85355397 x 539651255 x 170711985 x 10793
Negative: -1 x -21424105-5 x -4284821-43 x -498235-215 x -99647-251 x -85355-397 x -53965-1255 x -17071-1985 x -10793


How do I find the factor combinations of the number 21,424,105?

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 21,424,105, 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 21,424,105
-1 -21,424,105

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 21,424,105.

Example:
1 x 21,424,105 = 21,424,105
and
-1 x -21,424,105 = 21,424,105
Notice both answers equal 21,424,105

With that explanation out of the way, let's continue. Next, we take the number 21,424,105 and divide it by 2:

21,424,105 ÷ 2 = 10,712,052.5

If the quotient is a whole number, then 2 and 10,712,052.5 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 21,424,105
-1 -21,424,105

Now, we try dividing 21,424,105 by 3:

21,424,105 ÷ 3 = 7,141,368.3333

If the quotient is a whole number, then 3 and 7,141,368.3333 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 21,424,105
-1 -21,424,105

Let's try dividing by 4:

21,424,105 ÷ 4 = 5,356,026.25

If the quotient is a whole number, then 4 and 5,356,026.25 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 21,424,105
-1 21,424,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15432152513971,2551,98510,79317,07153,96585,35599,647498,2354,284,82121,424,105
-1-5-43-215-251-397-1,255-1,985-10,793-17,071-53,965-85,355-99,647-498,235-4,284,821-21,424,105

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