Q: What are the factor combinations of the number 123,023,329?

 A:
Positive:   1 x 12302332911 x 1118393913 x 946333341 x 3000569143 x 860303451 x 272779533 x 2308135863 x 20983
Negative: -1 x -123023329-11 x -11183939-13 x -9463333-41 x -3000569-143 x -860303-451 x -272779-533 x -230813-5863 x -20983


How do I find the factor combinations of the number 123,023,329?

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 123,023,329, 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.

1 123,023,329
-1 -123,023,329

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 123,023,329.

Example:
1 x 123,023,329 = 123,023,329
and
-1 x -123,023,329 = 123,023,329
Notice both answers equal 123,023,329

With that explanation out of the way, let's continue. Next, we take the number 123,023,329 and divide it by 2:

123,023,329 ÷ 2 = 61,511,664.5

If the quotient is a whole number, then 2 and 61,511,664.5 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:

1 123,023,329
-1 -123,023,329

Now, we try dividing 123,023,329 by 3:

123,023,329 ÷ 3 = 41,007,776.3333

If the quotient is a whole number, then 3 and 41,007,776.3333 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:

1 123,023,329
-1 -123,023,329

Let's try dividing by 4:

123,023,329 ÷ 4 = 30,755,832.25

If the quotient is a whole number, then 4 and 30,755,832.25 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:

1 123,023,329
-1 123,023,329
Keep dividing by the next highest number until you cannot divide anymore.

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

11113411434515335,86320,983230,813272,779860,3033,000,5699,463,33311,183,939123,023,329
-1-11-13-41-143-451-533-5,863-20,983-230,813-272,779-860,303-3,000,569-9,463,333-11,183,939-123,023,329

More Examples

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