Q: What are the factor combinations of the number 21,234,433?

 A:
Positive:   1 x 2123443311 x 193040341 x 517913197 x 107789239 x 88847451 x 470832167 x 97992629 x 8077
Negative: -1 x -21234433-11 x -1930403-41 x -517913-197 x -107789-239 x -88847-451 x -47083-2167 x -9799-2629 x -8077


How do I find the factor combinations of the number 21,234,433?

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 21,234,433, 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 21,234,433
-1 -21,234,433

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 21,234,433.

Example:
1 x 21,234,433 = 21,234,433
and
-1 x -21,234,433 = 21,234,433
Notice both answers equal 21,234,433

With that explanation out of the way, let's continue. Next, we take the number 21,234,433 and divide it by 2:

21,234,433 ÷ 2 = 10,617,216.5

If the quotient is a whole number, then 2 and 10,617,216.5 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 21,234,433
-1 -21,234,433

Now, we try dividing 21,234,433 by 3:

21,234,433 ÷ 3 = 7,078,144.3333

If the quotient is a whole number, then 3 and 7,078,144.3333 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 21,234,433
-1 -21,234,433

Let's try dividing by 4:

21,234,433 ÷ 4 = 5,308,608.25

If the quotient is a whole number, then 4 and 5,308,608.25 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 21,234,433
-1 21,234,433
Keep dividing by the next highest number until you cannot divide anymore.

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

111411972394512,1672,6298,0779,79947,08388,847107,789517,9131,930,40321,234,433
-1-11-41-197-239-451-2,167-2,629-8,077-9,799-47,083-88,847-107,789-517,913-1,930,403-21,234,433

More Examples

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