Q: What are the factor combinations of the number 23,124,431?

 A:
Positive:   1 x 2312443111 x 2102221121 x 191111223 x 103697857 x 269832453 x 9427
Negative: -1 x -23124431-11 x -2102221-121 x -191111-223 x -103697-857 x -26983-2453 x -9427


How do I find the factor combinations of the number 23,124,431?

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 23,124,431, 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 23,124,431
-1 -23,124,431

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 23,124,431.

Example:
1 x 23,124,431 = 23,124,431
and
-1 x -23,124,431 = 23,124,431
Notice both answers equal 23,124,431

With that explanation out of the way, let's continue. Next, we take the number 23,124,431 and divide it by 2:

23,124,431 ÷ 2 = 11,562,215.5

If the quotient is a whole number, then 2 and 11,562,215.5 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 23,124,431
-1 -23,124,431

Now, we try dividing 23,124,431 by 3:

23,124,431 ÷ 3 = 7,708,143.6667

If the quotient is a whole number, then 3 and 7,708,143.6667 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 23,124,431
-1 -23,124,431

Let's try dividing by 4:

23,124,431 ÷ 4 = 5,781,107.75

If the quotient is a whole number, then 4 and 5,781,107.75 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 23,124,431
-1 23,124,431
Keep dividing by the next highest number until you cannot divide anymore.

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

1111212238572,4539,42726,983103,697191,1112,102,22123,124,431
-1-11-121-223-857-2,453-9,427-26,983-103,697-191,111-2,102,221-23,124,431

More Examples

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