Q: What are the factor combinations of the number 21,201,233?

 A:
Positive:   1 x 2120123329 x 731077463 x 457911579 x 13427
Negative: -1 x -21201233-29 x -731077-463 x -45791-1579 x -13427


How do I find the factor combinations of the number 21,201,233?

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 21,201,233, 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 21,201,233
-1 -21,201,233

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 21,201,233.

Example:
1 x 21,201,233 = 21,201,233
and
-1 x -21,201,233 = 21,201,233
Notice both answers equal 21,201,233

With that explanation out of the way, let's continue. Next, we take the number 21,201,233 and divide it by 2:

21,201,233 ÷ 2 = 10,600,616.5

If the quotient is a whole number, then 2 and 10,600,616.5 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 21,201,233
-1 -21,201,233

Now, we try dividing 21,201,233 by 3:

21,201,233 ÷ 3 = 7,067,077.6667

If the quotient is a whole number, then 3 and 7,067,077.6667 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 21,201,233
-1 -21,201,233

Let's try dividing by 4:

21,201,233 ÷ 4 = 5,300,308.25

If the quotient is a whole number, then 4 and 5,300,308.25 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 21,201,233
-1 21,201,233
Keep dividing by the next highest number until you cannot divide anymore.

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

1294631,57913,42745,791731,07721,201,233
-1-29-463-1,579-13,427-45,791-731,077-21,201,233

More Examples

Here are some more numbers to try:

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