Q: What are the factor combinations of the number 199,856?

 A:
Positive:   1 x 1998562 x 999284 x 499648 x 2498216 x 12491
Negative: -1 x -199856-2 x -99928-4 x -49964-8 x -24982-16 x -12491


How do I find the factor combinations of the number 199,856?

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 199,856, 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.

1 199,856
-1 -199,856

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 199,856.

Example:
1 x 199,856 = 199,856
and
-1 x -199,856 = 199,856
Notice both answers equal 199,856

With that explanation out of the way, let's continue. Next, we take the number 199,856 and divide it by 2:

199,856 ÷ 2 = 99,928

If the quotient is a whole number, then 2 and 99,928 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 99,928 199,856
-1 -2 -99,928 -199,856

Now, we try dividing 199,856 by 3:

199,856 ÷ 3 = 66,618.6667

If the quotient is a whole number, then 3 and 66,618.6667 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 2 99,928 199,856
-1 -2 -99,928 -199,856

Let's try dividing by 4:

199,856 ÷ 4 = 49,964

If the quotient is a whole number, then 4 and 49,964 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 49,964 99,928 199,856
-1 -2 -4 -49,964 -99,928 199,856
Keep dividing by the next highest number until you cannot divide anymore.

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

12481612,49124,98249,96499,928199,856
-1-2-4-8-16-12,491-24,982-49,964-99,928-199,856

More Examples

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