Q: What are the factor combinations of the number 80,286?

 A:
Positive:   1 x 802862 x 401433 x 267626 x 13381
Negative: -1 x -80286-2 x -40143-3 x -26762-6 x -13381


How do I find the factor combinations of the number 80,286?

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 80,286, 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 80,286
-1 -80,286

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 80,286.

Example:
1 x 80,286 = 80,286
and
-1 x -80,286 = 80,286
Notice both answers equal 80,286

With that explanation out of the way, let's continue. Next, we take the number 80,286 and divide it by 2:

80,286 ÷ 2 = 40,143

If the quotient is a whole number, then 2 and 40,143 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 40,143 80,286
-1 -2 -40,143 -80,286

Now, we try dividing 80,286 by 3:

80,286 ÷ 3 = 26,762

If the quotient is a whole number, then 3 and 26,762 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 3 26,762 40,143 80,286
-1 -2 -3 -26,762 -40,143 -80,286

Let's try dividing by 4:

80,286 ÷ 4 = 20,071.5

If the quotient is a whole number, then 4 and 20,071.5 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 2 3 26,762 40,143 80,286
-1 -2 -3 -26,762 -40,143 80,286
Keep dividing by the next highest number until you cannot divide anymore.

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

123613,38126,76240,14380,286
-1-2-3-6-13,381-26,762-40,143-80,286

More Examples

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