Q: What are the factor combinations of the number 233,323,021?

 A:
Positive:   1 x 23332302119 x 12280159541 x 43128110279 x 22699
Negative: -1 x -233323021-19 x -12280159-541 x -431281-10279 x -22699


How do I find the factor combinations of the number 233,323,021?

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 233,323,021, 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.

1 233,323,021
-1 -233,323,021

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 233,323,021.

Example:
1 x 233,323,021 = 233,323,021
and
-1 x -233,323,021 = 233,323,021
Notice both answers equal 233,323,021

With that explanation out of the way, let's continue. Next, we take the number 233,323,021 and divide it by 2:

233,323,021 ÷ 2 = 116,661,510.5

If the quotient is a whole number, then 2 and 116,661,510.5 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:

1 233,323,021
-1 -233,323,021

Now, we try dividing 233,323,021 by 3:

233,323,021 ÷ 3 = 77,774,340.3333

If the quotient is a whole number, then 3 and 77,774,340.3333 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:

1 233,323,021
-1 -233,323,021

Let's try dividing by 4:

233,323,021 ÷ 4 = 58,330,755.25

If the quotient is a whole number, then 4 and 58,330,755.25 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:

1 233,323,021
-1 233,323,021
Keep dividing by the next highest number until you cannot divide anymore.

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

11954110,27922,699431,28112,280,159233,323,021
-1-19-541-10,279-22,699-431,281-12,280,159-233,323,021

More Examples

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