Q: What are the factor combinations of the number 100,512,217?

 A:
Positive:   1 x 10051221713 x 7731709431 x 2332075603 x 17939
Negative: -1 x -100512217-13 x -7731709-431 x -233207-5603 x -17939


How do I find the factor combinations of the number 100,512,217?

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 100,512,217, 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.

1 100,512,217
-1 -100,512,217

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 100,512,217.

Example:
1 x 100,512,217 = 100,512,217
and
-1 x -100,512,217 = 100,512,217
Notice both answers equal 100,512,217

With that explanation out of the way, let's continue. Next, we take the number 100,512,217 and divide it by 2:

100,512,217 ÷ 2 = 50,256,108.5

If the quotient is a whole number, then 2 and 50,256,108.5 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:

1 100,512,217
-1 -100,512,217

Now, we try dividing 100,512,217 by 3:

100,512,217 ÷ 3 = 33,504,072.3333

If the quotient is a whole number, then 3 and 33,504,072.3333 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:

1 100,512,217
-1 -100,512,217

Let's try dividing by 4:

100,512,217 ÷ 4 = 25,128,054.25

If the quotient is a whole number, then 4 and 25,128,054.25 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:

1 100,512,217
-1 100,512,217
Keep dividing by the next highest number until you cannot divide anymore.

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

1134315,60317,939233,2077,731,709100,512,217
-1-13-431-5,603-17,939-233,207-7,731,709-100,512,217

More Examples

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