Q: What are the factor combinations of the number 104,422,031?

 A:
Positive:   1 x 1044220317 x 1491743353 x 1970227149 x 700819371 x 2814611043 x 1001171889 x 552797897 x 13223
Negative: -1 x -104422031-7 x -14917433-53 x -1970227-149 x -700819-371 x -281461-1043 x -100117-1889 x -55279-7897 x -13223


How do I find the factor combinations of the number 104,422,031?

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 104,422,031, 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.

1 104,422,031
-1 -104,422,031

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 104,422,031.

Example:
1 x 104,422,031 = 104,422,031
and
-1 x -104,422,031 = 104,422,031
Notice both answers equal 104,422,031

With that explanation out of the way, let's continue. Next, we take the number 104,422,031 and divide it by 2:

104,422,031 ÷ 2 = 52,211,015.5

If the quotient is a whole number, then 2 and 52,211,015.5 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:

1 104,422,031
-1 -104,422,031

Now, we try dividing 104,422,031 by 3:

104,422,031 ÷ 3 = 34,807,343.6667

If the quotient is a whole number, then 3 and 34,807,343.6667 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:

1 104,422,031
-1 -104,422,031

Let's try dividing by 4:

104,422,031 ÷ 4 = 26,105,507.75

If the quotient is a whole number, then 4 and 26,105,507.75 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:

1 104,422,031
-1 104,422,031
Keep dividing by the next highest number until you cannot divide anymore.

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

17531493711,0431,8897,89713,22355,279100,117281,461700,8191,970,22714,917,433104,422,031
-1-7-53-149-371-1,043-1,889-7,897-13,223-55,279-100,117-281,461-700,819-1,970,227-14,917,433-104,422,031

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