Q: What are the factor combinations of the number 188,108?

 A:
Positive:   1 x 1881082 x 940544 x 4702731 x 606837 x 508441 x 458862 x 303474 x 254282 x 2294124 x 1517148 x 1271164 x 1147
Negative: -1 x -188108-2 x -94054-4 x -47027-31 x -6068-37 x -5084-41 x -4588-62 x -3034-74 x -2542-82 x -2294-124 x -1517-148 x -1271-164 x -1147


How do I find the factor combinations of the number 188,108?

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 188,108, 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.

1 188,108
-1 -188,108

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 188,108.

Example:
1 x 188,108 = 188,108
and
-1 x -188,108 = 188,108
Notice both answers equal 188,108

With that explanation out of the way, let's continue. Next, we take the number 188,108 and divide it by 2:

188,108 ÷ 2 = 94,054

If the quotient is a whole number, then 2 and 94,054 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 94,054 188,108
-1 -2 -94,054 -188,108

Now, we try dividing 188,108 by 3:

188,108 ÷ 3 = 62,702.6667

If the quotient is a whole number, then 3 and 62,702.6667 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 2 94,054 188,108
-1 -2 -94,054 -188,108

Let's try dividing by 4:

188,108 ÷ 4 = 47,027

If the quotient is a whole number, then 4 and 47,027 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 4 47,027 94,054 188,108
-1 -2 -4 -47,027 -94,054 188,108
Keep dividing by the next highest number until you cannot divide anymore.

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

1243137416274821241481641,1471,2711,5172,2942,5423,0344,5885,0846,06847,02794,054188,108
-1-2-4-31-37-41-62-74-82-124-148-164-1,147-1,271-1,517-2,294-2,542-3,034-4,588-5,084-6,068-47,027-94,054-188,108

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