Q: What are the factor combinations of the number 66,883?

 A:
Positive:   1 x 66883
Negative: -1 x -66883


How do I find the factor combinations of the number 66,883?

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 66,883, 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 66,883
-1 -66,883

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 66,883.

Example:
1 x 66,883 = 66,883
and
-1 x -66,883 = 66,883
Notice both answers equal 66,883

With that explanation out of the way, let's continue. Next, we take the number 66,883 and divide it by 2:

66,883 ÷ 2 = 33,441.5

If the quotient is a whole number, then 2 and 33,441.5 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 66,883
-1 -66,883

Now, we try dividing 66,883 by 3:

66,883 ÷ 3 = 22,294.3333

If the quotient is a whole number, then 3 and 22,294.3333 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 66,883
-1 -66,883

Let's try dividing by 4:

66,883 ÷ 4 = 16,720.75

If the quotient is a whole number, then 4 and 16,720.75 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 66,883
-1 66,883
Keep dividing by the next highest number until you cannot divide anymore.

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

166,883
-1-66,883

More Examples

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