Q: What are the factor combinations of the number 21,404,317?

 A:
Positive:   1 x 2140431711 x 194584719 x 112654347 x 455411209 x 102413517 x 41401893 x 239692179 x 9823
Negative: -1 x -21404317-11 x -1945847-19 x -1126543-47 x -455411-209 x -102413-517 x -41401-893 x -23969-2179 x -9823


How do I find the factor combinations of the number 21,404,317?

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 21,404,317, 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 21,404,317
-1 -21,404,317

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 21,404,317.

Example:
1 x 21,404,317 = 21,404,317
and
-1 x -21,404,317 = 21,404,317
Notice both answers equal 21,404,317

With that explanation out of the way, let's continue. Next, we take the number 21,404,317 and divide it by 2:

21,404,317 ÷ 2 = 10,702,158.5

If the quotient is a whole number, then 2 and 10,702,158.5 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 21,404,317
-1 -21,404,317

Now, we try dividing 21,404,317 by 3:

21,404,317 ÷ 3 = 7,134,772.3333

If the quotient is a whole number, then 3 and 7,134,772.3333 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 21,404,317
-1 -21,404,317

Let's try dividing by 4:

21,404,317 ÷ 4 = 5,351,079.25

If the quotient is a whole number, then 4 and 5,351,079.25 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 21,404,317
-1 21,404,317
Keep dividing by the next highest number until you cannot divide anymore.

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

11119472095178932,1799,82323,96941,401102,413455,4111,126,5431,945,84721,404,317
-1-11-19-47-209-517-893-2,179-9,823-23,969-41,401-102,413-455,411-1,126,543-1,945,847-21,404,317

More Examples

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