Q: What are the factor combinations of the number 123,132,233?

 A:
Positive:   1 x 1231322337 x 1759031959 x 2086987281 x 438193413 x 2981411061 x 1160531967 x 625997427 x 16579
Negative: -1 x -123132233-7 x -17590319-59 x -2086987-281 x -438193-413 x -298141-1061 x -116053-1967 x -62599-7427 x -16579


How do I find the factor combinations of the number 123,132,233?

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 123,132,233, 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.

1 123,132,233
-1 -123,132,233

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 123,132,233.

Example:
1 x 123,132,233 = 123,132,233
and
-1 x -123,132,233 = 123,132,233
Notice both answers equal 123,132,233

With that explanation out of the way, let's continue. Next, we take the number 123,132,233 and divide it by 2:

123,132,233 ÷ 2 = 61,566,116.5

If the quotient is a whole number, then 2 and 61,566,116.5 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:

1 123,132,233
-1 -123,132,233

Now, we try dividing 123,132,233 by 3:

123,132,233 ÷ 3 = 41,044,077.6667

If the quotient is a whole number, then 3 and 41,044,077.6667 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:

1 123,132,233
-1 -123,132,233

Let's try dividing by 4:

123,132,233 ÷ 4 = 30,783,058.25

If the quotient is a whole number, then 4 and 30,783,058.25 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:

1 123,132,233
-1 123,132,233
Keep dividing by the next highest number until you cannot divide anymore.

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

17592814131,0611,9677,42716,57962,599116,053298,141438,1932,086,98717,590,319123,132,233
-1-7-59-281-413-1,061-1,967-7,427-16,579-62,599-116,053-298,141-438,193-2,086,987-17,590,319-123,132,233

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