Q: What are the factor combinations of the number 21,441,469?

 A:
Positive:   1 x 214414697 x 306306729 x 73936149 x 43758179 x 271411191 x 112259203 x 105623553 x 387731337 x 160371421 x 150892291 x 93593871 x 5539
Negative: -1 x -21441469-7 x -3063067-29 x -739361-49 x -437581-79 x -271411-191 x -112259-203 x -105623-553 x -38773-1337 x -16037-1421 x -15089-2291 x -9359-3871 x -5539


How do I find the factor combinations of the number 21,441,469?

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 21,441,469, 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 21,441,469
-1 -21,441,469

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 21,441,469.

Example:
1 x 21,441,469 = 21,441,469
and
-1 x -21,441,469 = 21,441,469
Notice both answers equal 21,441,469

With that explanation out of the way, let's continue. Next, we take the number 21,441,469 and divide it by 2:

21,441,469 ÷ 2 = 10,720,734.5

If the quotient is a whole number, then 2 and 10,720,734.5 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 21,441,469
-1 -21,441,469

Now, we try dividing 21,441,469 by 3:

21,441,469 ÷ 3 = 7,147,156.3333

If the quotient is a whole number, then 3 and 7,147,156.3333 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 21,441,469
-1 -21,441,469

Let's try dividing by 4:

21,441,469 ÷ 4 = 5,360,367.25

If the quotient is a whole number, then 4 and 5,360,367.25 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 21,441,469
-1 21,441,469
Keep dividing by the next highest number until you cannot divide anymore.

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

172949791912035531,3371,4212,2913,8715,5399,35915,08916,03738,773105,623112,259271,411437,581739,3613,063,06721,441,469
-1-7-29-49-79-191-203-553-1,337-1,421-2,291-3,871-5,539-9,359-15,089-16,037-38,773-105,623-112,259-271,411-437,581-739,361-3,063,067-21,441,469

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