Q: What are the factor combinations of the number 38,404,091?

 A:
Positive:   1 x 3840409111 x 349128129 x 1324279131 x 293161319 x 120389919 x 417891441 x 266513799 x 10109
Negative: -1 x -38404091-11 x -3491281-29 x -1324279-131 x -293161-319 x -120389-919 x -41789-1441 x -26651-3799 x -10109


How do I find the factor combinations of the number 38,404,091?

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 38,404,091, 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 38,404,091
-1 -38,404,091

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 38,404,091.

Example:
1 x 38,404,091 = 38,404,091
and
-1 x -38,404,091 = 38,404,091
Notice both answers equal 38,404,091

With that explanation out of the way, let's continue. Next, we take the number 38,404,091 and divide it by 2:

38,404,091 ÷ 2 = 19,202,045.5

If the quotient is a whole number, then 2 and 19,202,045.5 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 38,404,091
-1 -38,404,091

Now, we try dividing 38,404,091 by 3:

38,404,091 ÷ 3 = 12,801,363.6667

If the quotient is a whole number, then 3 and 12,801,363.6667 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 38,404,091
-1 -38,404,091

Let's try dividing by 4:

38,404,091 ÷ 4 = 9,601,022.75

If the quotient is a whole number, then 4 and 9,601,022.75 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 38,404,091
-1 38,404,091
Keep dividing by the next highest number until you cannot divide anymore.

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

111291313199191,4413,79910,10926,65141,789120,389293,1611,324,2793,491,28138,404,091
-1-11-29-131-319-919-1,441-3,799-10,109-26,651-41,789-120,389-293,161-1,324,279-3,491,281-38,404,091

More Examples

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