Q: What are the factor combinations of the number 23,115,323?

 A:
Positive:   1 x 231153237 x 330218911 x 210139377 x 300199317 x 72919947 x 244092219 x 104173487 x 6629
Negative: -1 x -23115323-7 x -3302189-11 x -2101393-77 x -300199-317 x -72919-947 x -24409-2219 x -10417-3487 x -6629


How do I find the factor combinations of the number 23,115,323?

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 23,115,323, 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 23,115,323
-1 -23,115,323

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 23,115,323.

Example:
1 x 23,115,323 = 23,115,323
and
-1 x -23,115,323 = 23,115,323
Notice both answers equal 23,115,323

With that explanation out of the way, let's continue. Next, we take the number 23,115,323 and divide it by 2:

23,115,323 ÷ 2 = 11,557,661.5

If the quotient is a whole number, then 2 and 11,557,661.5 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 23,115,323
-1 -23,115,323

Now, we try dividing 23,115,323 by 3:

23,115,323 ÷ 3 = 7,705,107.6667

If the quotient is a whole number, then 3 and 7,705,107.6667 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 23,115,323
-1 -23,115,323

Let's try dividing by 4:

23,115,323 ÷ 4 = 5,778,830.75

If the quotient is a whole number, then 4 and 5,778,830.75 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 23,115,323
-1 23,115,323
Keep dividing by the next highest number until you cannot divide anymore.

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

1711773179472,2193,4876,62910,41724,40972,919300,1992,101,3933,302,18923,115,323
-1-7-11-77-317-947-2,219-3,487-6,629-10,417-24,409-72,919-300,199-2,101,393-3,302,189-23,115,323

More Examples

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