Q: What are the factor combinations of the number 199,855?

 A:
Positive:   1 x 1998555 x 39971
Negative: -1 x -199855-5 x -39971


How do I find the factor combinations of the number 199,855?

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 199,855, 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.

1 199,855
-1 -199,855

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 199,855.

Example:
1 x 199,855 = 199,855
and
-1 x -199,855 = 199,855
Notice both answers equal 199,855

With that explanation out of the way, let's continue. Next, we take the number 199,855 and divide it by 2:

199,855 ÷ 2 = 99,927.5

If the quotient is a whole number, then 2 and 99,927.5 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:

1 199,855
-1 -199,855

Now, we try dividing 199,855 by 3:

199,855 ÷ 3 = 66,618.3333

If the quotient is a whole number, then 3 and 66,618.3333 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:

1 199,855
-1 -199,855

Let's try dividing by 4:

199,855 ÷ 4 = 49,963.75

If the quotient is a whole number, then 4 and 49,963.75 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:

1 199,855
-1 199,855
Keep dividing by the next highest number until you cannot divide anymore.

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

1539,971199,855
-1-5-39,971-199,855

More Examples

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