Q: What are the factor combinations of the number 104,231,131?

 A:
Positive:   1 x 10423113117 x 613124319 x 5485849323 x 322697467 x 223193691 x 1508417939 x 131298873 x 11747
Negative: -1 x -104231131-17 x -6131243-19 x -5485849-323 x -322697-467 x -223193-691 x -150841-7939 x -13129-8873 x -11747


How do I find the factor combinations of the number 104,231,131?

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 104,231,131, 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.

1 104,231,131
-1 -104,231,131

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 104,231,131.

Example:
1 x 104,231,131 = 104,231,131
and
-1 x -104,231,131 = 104,231,131
Notice both answers equal 104,231,131

With that explanation out of the way, let's continue. Next, we take the number 104,231,131 and divide it by 2:

104,231,131 ÷ 2 = 52,115,565.5

If the quotient is a whole number, then 2 and 52,115,565.5 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:

1 104,231,131
-1 -104,231,131

Now, we try dividing 104,231,131 by 3:

104,231,131 ÷ 3 = 34,743,710.3333

If the quotient is a whole number, then 3 and 34,743,710.3333 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:

1 104,231,131
-1 -104,231,131

Let's try dividing by 4:

104,231,131 ÷ 4 = 26,057,782.75

If the quotient is a whole number, then 4 and 26,057,782.75 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:

1 104,231,131
-1 104,231,131
Keep dividing by the next highest number until you cannot divide anymore.

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

117193234676917,9398,87311,74713,129150,841223,193322,6975,485,8496,131,243104,231,131
-1-17-19-323-467-691-7,939-8,873-11,747-13,129-150,841-223,193-322,697-5,485,849-6,131,243-104,231,131

More Examples

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