Q: What are the factor combinations of the number 101,100,133?

 A:
Positive:   1 x 101100133
Negative: -1 x -101100133


How do I find the factor combinations of the number 101,100,133?

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 101,100,133, 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.

1 101,100,133
-1 -101,100,133

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 101,100,133.

Example:
1 x 101,100,133 = 101,100,133
and
-1 x -101,100,133 = 101,100,133
Notice both answers equal 101,100,133

With that explanation out of the way, let's continue. Next, we take the number 101,100,133 and divide it by 2:

101,100,133 ÷ 2 = 50,550,066.5

If the quotient is a whole number, then 2 and 50,550,066.5 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:

1 101,100,133
-1 -101,100,133

Now, we try dividing 101,100,133 by 3:

101,100,133 ÷ 3 = 33,700,044.3333

If the quotient is a whole number, then 3 and 33,700,044.3333 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:

1 101,100,133
-1 -101,100,133

Let's try dividing by 4:

101,100,133 ÷ 4 = 25,275,033.25

If the quotient is a whole number, then 4 and 25,275,033.25 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:

1 101,100,133
-1 101,100,133
Keep dividing by the next highest number until you cannot divide anymore.

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

1101,100,133
-1-101,100,133

More Examples

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