Q: What are the factor combinations of the number 21,010,249?

 A:
Positive:   1 x 2101024913 x 161617317 x 123589771 x 295919103 x 203983169 x 124321221 x 95069923 x 227631207 x 174071339 x 156911751 x 119992873 x 7313
Negative: -1 x -21010249-13 x -1616173-17 x -1235897-71 x -295919-103 x -203983-169 x -124321-221 x -95069-923 x -22763-1207 x -17407-1339 x -15691-1751 x -11999-2873 x -7313


How do I find the factor combinations of the number 21,010,249?

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 21,010,249, 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 21,010,249
-1 -21,010,249

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 21,010,249.

Example:
1 x 21,010,249 = 21,010,249
and
-1 x -21,010,249 = 21,010,249
Notice both answers equal 21,010,249

With that explanation out of the way, let's continue. Next, we take the number 21,010,249 and divide it by 2:

21,010,249 ÷ 2 = 10,505,124.5

If the quotient is a whole number, then 2 and 10,505,124.5 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 21,010,249
-1 -21,010,249

Now, we try dividing 21,010,249 by 3:

21,010,249 ÷ 3 = 7,003,416.3333

If the quotient is a whole number, then 3 and 7,003,416.3333 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 21,010,249
-1 -21,010,249

Let's try dividing by 4:

21,010,249 ÷ 4 = 5,252,562.25

If the quotient is a whole number, then 4 and 5,252,562.25 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 21,010,249
-1 21,010,249
Keep dividing by the next highest number until you cannot divide anymore.

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

11317711031692219231,2071,3391,7512,8737,31311,99915,69117,40722,76395,069124,321203,983295,9191,235,8971,616,17321,010,249
-1-13-17-71-103-169-221-923-1,207-1,339-1,751-2,873-7,313-11,999-15,691-17,407-22,763-95,069-124,321-203,983-295,919-1,235,897-1,616,173-21,010,249

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