Q: What are the factor combinations of the number 123,200,231?

 A:
Positive:   1 x 1232002317 x 1760003311 x 1120002131 x 397420177 x 1600003217 x 567743341 x 3612912387 x 51613
Negative: -1 x -123200231-7 x -17600033-11 x -11200021-31 x -3974201-77 x -1600003-217 x -567743-341 x -361291-2387 x -51613


How do I find the factor combinations of the number 123,200,231?

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 123,200,231, 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.

1 123,200,231
-1 -123,200,231

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 123,200,231.

Example:
1 x 123,200,231 = 123,200,231
and
-1 x -123,200,231 = 123,200,231
Notice both answers equal 123,200,231

With that explanation out of the way, let's continue. Next, we take the number 123,200,231 and divide it by 2:

123,200,231 ÷ 2 = 61,600,115.5

If the quotient is a whole number, then 2 and 61,600,115.5 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:

1 123,200,231
-1 -123,200,231

Now, we try dividing 123,200,231 by 3:

123,200,231 ÷ 3 = 41,066,743.6667

If the quotient is a whole number, then 3 and 41,066,743.6667 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:

1 123,200,231
-1 -123,200,231

Let's try dividing by 4:

123,200,231 ÷ 4 = 30,800,057.75

If the quotient is a whole number, then 4 and 30,800,057.75 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:

1 123,200,231
-1 123,200,231
Keep dividing by the next highest number until you cannot divide anymore.

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

171131772173412,38751,613361,291567,7431,600,0033,974,20111,200,02117,600,033123,200,231
-1-7-11-31-77-217-341-2,387-51,613-361,291-567,743-1,600,003-3,974,201-11,200,021-17,600,033-123,200,231

More Examples

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