Q: What are the factor combinations of the number 21,021,325?

 A:
Positive:   1 x 210213255 x 420426513 x 161702525 x 84085365 x 32340571 x 296075325 x 64681355 x 59215911 x 23075923 x 227751775 x 118434555 x 4615
Negative: -1 x -21021325-5 x -4204265-13 x -1617025-25 x -840853-65 x -323405-71 x -296075-325 x -64681-355 x -59215-911 x -23075-923 x -22775-1775 x -11843-4555 x -4615


How do I find the factor combinations of the number 21,021,325?

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 21,021,325, 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 21,021,325
-1 -21,021,325

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 21,021,325.

Example:
1 x 21,021,325 = 21,021,325
and
-1 x -21,021,325 = 21,021,325
Notice both answers equal 21,021,325

With that explanation out of the way, let's continue. Next, we take the number 21,021,325 and divide it by 2:

21,021,325 ÷ 2 = 10,510,662.5

If the quotient is a whole number, then 2 and 10,510,662.5 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 21,021,325
-1 -21,021,325

Now, we try dividing 21,021,325 by 3:

21,021,325 ÷ 3 = 7,007,108.3333

If the quotient is a whole number, then 3 and 7,007,108.3333 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 21,021,325
-1 -21,021,325

Let's try dividing by 4:

21,021,325 ÷ 4 = 5,255,331.25

If the quotient is a whole number, then 4 and 5,255,331.25 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 21,021,325
-1 21,021,325
Keep dividing by the next highest number until you cannot divide anymore.

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

15132565713253559119231,7754,5554,61511,84322,77523,07559,21564,681296,075323,405840,8531,617,0254,204,26521,021,325
-1-5-13-25-65-71-325-355-911-923-1,775-4,555-4,615-11,843-22,775-23,075-59,215-64,681-296,075-323,405-840,853-1,617,025-4,204,265-21,021,325

More Examples

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