Q: What are the factor combinations of the number 186,989?

 A:
Positive:   1 x 18698911 x 1699989 x 2101191 x 979
Negative: -1 x -186989-11 x -16999-89 x -2101-191 x -979


How do I find the factor combinations of the number 186,989?

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 186,989, 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.

1 186,989
-1 -186,989

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 186,989.

Example:
1 x 186,989 = 186,989
and
-1 x -186,989 = 186,989
Notice both answers equal 186,989

With that explanation out of the way, let's continue. Next, we take the number 186,989 and divide it by 2:

186,989 ÷ 2 = 93,494.5

If the quotient is a whole number, then 2 and 93,494.5 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:

1 186,989
-1 -186,989

Now, we try dividing 186,989 by 3:

186,989 ÷ 3 = 62,329.6667

If the quotient is a whole number, then 3 and 62,329.6667 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:

1 186,989
-1 -186,989

Let's try dividing by 4:

186,989 ÷ 4 = 46,747.25

If the quotient is a whole number, then 4 and 46,747.25 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:

1 186,989
-1 186,989
Keep dividing by the next highest number until you cannot divide anymore.

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

111891919792,10116,999186,989
-1-11-89-191-979-2,101-16,999-186,989

More Examples

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