Q: What are the factor combinations of the number 100,431,133?

 A:
Positive:   1 x 10043113311 x 913010323 x 436657171 x 1414523253 x 396961781 x 1285931633 x 615015591 x 17963
Negative: -1 x -100431133-11 x -9130103-23 x -4366571-71 x -1414523-253 x -396961-781 x -128593-1633 x -61501-5591 x -17963


How do I find the factor combinations of the number 100,431,133?

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 100,431,133, 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.

1 100,431,133
-1 -100,431,133

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 100,431,133.

Example:
1 x 100,431,133 = 100,431,133
and
-1 x -100,431,133 = 100,431,133
Notice both answers equal 100,431,133

With that explanation out of the way, let's continue. Next, we take the number 100,431,133 and divide it by 2:

100,431,133 ÷ 2 = 50,215,566.5

If the quotient is a whole number, then 2 and 50,215,566.5 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:

1 100,431,133
-1 -100,431,133

Now, we try dividing 100,431,133 by 3:

100,431,133 ÷ 3 = 33,477,044.3333

If the quotient is a whole number, then 3 and 33,477,044.3333 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:

1 100,431,133
-1 -100,431,133

Let's try dividing by 4:

100,431,133 ÷ 4 = 25,107,783.25

If the quotient is a whole number, then 4 and 25,107,783.25 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:

1 100,431,133
-1 100,431,133
Keep dividing by the next highest number until you cannot divide anymore.

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

11123712537811,6335,59117,96361,501128,593396,9611,414,5234,366,5719,130,103100,431,133
-1-11-23-71-253-781-1,633-5,591-17,963-61,501-128,593-396,961-1,414,523-4,366,571-9,130,103-100,431,133

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