Q: What are the factor combinations of the number 10,861?

 A:
Positive:   1 x 10861
Negative: -1 x -10861


How do I find the factor combinations of the number 10,861?

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 10,861, 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 10,861
-1 -10,861

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 10,861.

Example:
1 x 10,861 = 10,861
and
-1 x -10,861 = 10,861
Notice both answers equal 10,861

With that explanation out of the way, let's continue. Next, we take the number 10,861 and divide it by 2:

10,861 ÷ 2 = 5,430.5

If the quotient is a whole number, then 2 and 5,430.5 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 10,861
-1 -10,861

Now, we try dividing 10,861 by 3:

10,861 ÷ 3 = 3,620.3333

If the quotient is a whole number, then 3 and 3,620.3333 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 10,861
-1 -10,861

Let's try dividing by 4:

10,861 ÷ 4 = 2,715.25

If the quotient is a whole number, then 4 and 2,715.25 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 10,861
-1 10,861
Keep dividing by the next highest number until you cannot divide anymore.

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

110,861
-1-10,861

More Examples

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