Q: What are the factor combinations of the number 23,021,315?

 A:
Positive:   1 x 230213155 x 460426317 x 135419585 x 270839199 x 115685995 x 231371361 x 169153383 x 6805
Negative: -1 x -23021315-5 x -4604263-17 x -1354195-85 x -270839-199 x -115685-995 x -23137-1361 x -16915-3383 x -6805


How do I find the factor combinations of the number 23,021,315?

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 23,021,315, 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 23,021,315
-1 -23,021,315

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 23,021,315.

Example:
1 x 23,021,315 = 23,021,315
and
-1 x -23,021,315 = 23,021,315
Notice both answers equal 23,021,315

With that explanation out of the way, let's continue. Next, we take the number 23,021,315 and divide it by 2:

23,021,315 ÷ 2 = 11,510,657.5

If the quotient is a whole number, then 2 and 11,510,657.5 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 23,021,315
-1 -23,021,315

Now, we try dividing 23,021,315 by 3:

23,021,315 ÷ 3 = 7,673,771.6667

If the quotient is a whole number, then 3 and 7,673,771.6667 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 23,021,315
-1 -23,021,315

Let's try dividing by 4:

23,021,315 ÷ 4 = 5,755,328.75

If the quotient is a whole number, then 4 and 5,755,328.75 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 23,021,315
-1 23,021,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1517851999951,3613,3836,80516,91523,137115,685270,8391,354,1954,604,26323,021,315
-1-5-17-85-199-995-1,361-3,383-6,805-16,915-23,137-115,685-270,839-1,354,195-4,604,263-23,021,315

More Examples

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