Q: What are the factor combinations of the number 100,230,217?

 A:
Positive:   1 x 100230217107 x 936731
Negative: -1 x -100230217-107 x -936731


How do I find the factor combinations of the number 100,230,217?

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 100,230,217, 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.

1 100,230,217
-1 -100,230,217

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 100,230,217.

Example:
1 x 100,230,217 = 100,230,217
and
-1 x -100,230,217 = 100,230,217
Notice both answers equal 100,230,217

With that explanation out of the way, let's continue. Next, we take the number 100,230,217 and divide it by 2:

100,230,217 ÷ 2 = 50,115,108.5

If the quotient is a whole number, then 2 and 50,115,108.5 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:

1 100,230,217
-1 -100,230,217

Now, we try dividing 100,230,217 by 3:

100,230,217 ÷ 3 = 33,410,072.3333

If the quotient is a whole number, then 3 and 33,410,072.3333 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:

1 100,230,217
-1 -100,230,217

Let's try dividing by 4:

100,230,217 ÷ 4 = 25,057,554.25

If the quotient is a whole number, then 4 and 25,057,554.25 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:

1 100,230,217
-1 100,230,217
Keep dividing by the next highest number until you cannot divide anymore.

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

1107936,731100,230,217
-1-107-936,731-100,230,217

More Examples

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