Q: What are the factor combinations of the number 68,021?

 A:
Positive:   1 x 68021251 x 271
Negative: -1 x -68021-251 x -271


How do I find the factor combinations of the number 68,021?

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 68,021, 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 68,021
-1 -68,021

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 68,021.

Example:
1 x 68,021 = 68,021
and
-1 x -68,021 = 68,021
Notice both answers equal 68,021

With that explanation out of the way, let's continue. Next, we take the number 68,021 and divide it by 2:

68,021 ÷ 2 = 34,010.5

If the quotient is a whole number, then 2 and 34,010.5 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 68,021
-1 -68,021

Now, we try dividing 68,021 by 3:

68,021 ÷ 3 = 22,673.6667

If the quotient is a whole number, then 3 and 22,673.6667 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 68,021
-1 -68,021

Let's try dividing by 4:

68,021 ÷ 4 = 17,005.25

If the quotient is a whole number, then 4 and 17,005.25 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 68,021
-1 68,021
Keep dividing by the next highest number until you cannot divide anymore.

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

125127168,021
-1-251-271-68,021

More Examples

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