Q: What are the factor combinations of the number 108,661?

 A:
Positive:   1 x 1086617 x 1552319 x 571943 x 2527133 x 817301 x 361
Negative: -1 x -108661-7 x -15523-19 x -5719-43 x -2527-133 x -817-301 x -361


How do I find the factor combinations of the number 108,661?

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 108,661, 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.

1 108,661
-1 -108,661

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 108,661.

Example:
1 x 108,661 = 108,661
and
-1 x -108,661 = 108,661
Notice both answers equal 108,661

With that explanation out of the way, let's continue. Next, we take the number 108,661 and divide it by 2:

108,661 ÷ 2 = 54,330.5

If the quotient is a whole number, then 2 and 54,330.5 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:

1 108,661
-1 -108,661

Now, we try dividing 108,661 by 3:

108,661 ÷ 3 = 36,220.3333

If the quotient is a whole number, then 3 and 36,220.3333 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:

1 108,661
-1 -108,661

Let's try dividing by 4:

108,661 ÷ 4 = 27,165.25

If the quotient is a whole number, then 4 and 27,165.25 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:

1 108,661
-1 108,661
Keep dividing by the next highest number until you cannot divide anymore.

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

1719431333013618172,5275,71915,523108,661
-1-7-19-43-133-301-361-817-2,527-5,719-15,523-108,661

More Examples

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