Q: What are the factor combinations of the number 23,528,791?

 A:
Positive:   1 x 2352879111 x 213898113 x 1809907137 x 171743143 x 1645371201 x 195911507 x 156131781 x 13211
Negative: -1 x -23528791-11 x -2138981-13 x -1809907-137 x -171743-143 x -164537-1201 x -19591-1507 x -15613-1781 x -13211


How do I find the factor combinations of the number 23,528,791?

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 23,528,791, 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 23,528,791
-1 -23,528,791

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 23,528,791.

Example:
1 x 23,528,791 = 23,528,791
and
-1 x -23,528,791 = 23,528,791
Notice both answers equal 23,528,791

With that explanation out of the way, let's continue. Next, we take the number 23,528,791 and divide it by 2:

23,528,791 ÷ 2 = 11,764,395.5

If the quotient is a whole number, then 2 and 11,764,395.5 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 23,528,791
-1 -23,528,791

Now, we try dividing 23,528,791 by 3:

23,528,791 ÷ 3 = 7,842,930.3333

If the quotient is a whole number, then 3 and 7,842,930.3333 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 23,528,791
-1 -23,528,791

Let's try dividing by 4:

23,528,791 ÷ 4 = 5,882,197.75

If the quotient is a whole number, then 4 and 5,882,197.75 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 23,528,791
-1 23,528,791
Keep dividing by the next highest number until you cannot divide anymore.

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

111131371431,2011,5071,78113,21115,61319,591164,537171,7431,809,9072,138,98123,528,791
-1-11-13-137-143-1,201-1,507-1,781-13,211-15,613-19,591-164,537-171,743-1,809,907-2,138,981-23,528,791

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