Q: What are the factor combinations of the number 23,231,135?

 A:
Positive:   1 x 232311355 x 464622779 x 294065103 x 225545395 x 58813515 x 45109571 x 406852855 x 8137
Negative: -1 x -23231135-5 x -4646227-79 x -294065-103 x -225545-395 x -58813-515 x -45109-571 x -40685-2855 x -8137


How do I find the factor combinations of the number 23,231,135?

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 23,231,135, 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 23,231,135
-1 -23,231,135

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 23,231,135.

Example:
1 x 23,231,135 = 23,231,135
and
-1 x -23,231,135 = 23,231,135
Notice both answers equal 23,231,135

With that explanation out of the way, let's continue. Next, we take the number 23,231,135 and divide it by 2:

23,231,135 ÷ 2 = 11,615,567.5

If the quotient is a whole number, then 2 and 11,615,567.5 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 23,231,135
-1 -23,231,135

Now, we try dividing 23,231,135 by 3:

23,231,135 ÷ 3 = 7,743,711.6667

If the quotient is a whole number, then 3 and 7,743,711.6667 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 23,231,135
-1 -23,231,135

Let's try dividing by 4:

23,231,135 ÷ 4 = 5,807,783.75

If the quotient is a whole number, then 4 and 5,807,783.75 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 23,231,135
-1 23,231,135
Keep dividing by the next highest number until you cannot divide anymore.

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

15791033955155712,8558,13740,68545,10958,813225,545294,0654,646,22723,231,135
-1-5-79-103-395-515-571-2,855-8,137-40,685-45,109-58,813-225,545-294,065-4,646,227-23,231,135

More Examples

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