Q: What are the factor combinations of the number 123,023,303?

 A:
Positive:   1 x 12302330313 x 946333179 x 1557257103 x 11944011027 x 1197891163 x 1057811339 x 918778137 x 15119
Negative: -1 x -123023303-13 x -9463331-79 x -1557257-103 x -1194401-1027 x -119789-1163 x -105781-1339 x -91877-8137 x -15119


How do I find the factor combinations of the number 123,023,303?

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 123,023,303, 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.

1 123,023,303
-1 -123,023,303

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 123,023,303.

Example:
1 x 123,023,303 = 123,023,303
and
-1 x -123,023,303 = 123,023,303
Notice both answers equal 123,023,303

With that explanation out of the way, let's continue. Next, we take the number 123,023,303 and divide it by 2:

123,023,303 ÷ 2 = 61,511,651.5

If the quotient is a whole number, then 2 and 61,511,651.5 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:

1 123,023,303
-1 -123,023,303

Now, we try dividing 123,023,303 by 3:

123,023,303 ÷ 3 = 41,007,767.6667

If the quotient is a whole number, then 3 and 41,007,767.6667 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:

1 123,023,303
-1 -123,023,303

Let's try dividing by 4:

123,023,303 ÷ 4 = 30,755,825.75

If the quotient is a whole number, then 4 and 30,755,825.75 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:

1 123,023,303
-1 123,023,303
Keep dividing by the next highest number until you cannot divide anymore.

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

113791031,0271,1631,3398,13715,11991,877105,781119,7891,194,4011,557,2579,463,331123,023,303
-1-13-79-103-1,027-1,163-1,339-8,137-15,119-91,877-105,781-119,789-1,194,401-1,557,257-9,463,331-123,023,303

More Examples

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