Q: What are the factor combinations of the number 109,076?

 A:
Positive:   1 x 1090762 x 545384 x 2726911 x 991622 x 495837 x 294844 x 247967 x 162874 x 1474134 x 814148 x 737268 x 407
Negative: -1 x -109076-2 x -54538-4 x -27269-11 x -9916-22 x -4958-37 x -2948-44 x -2479-67 x -1628-74 x -1474-134 x -814-148 x -737-268 x -407


How do I find the factor combinations of the number 109,076?

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 109,076, 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.

1 109,076
-1 -109,076

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 109,076.

Example:
1 x 109,076 = 109,076
and
-1 x -109,076 = 109,076
Notice both answers equal 109,076

With that explanation out of the way, let's continue. Next, we take the number 109,076 and divide it by 2:

109,076 ÷ 2 = 54,538

If the quotient is a whole number, then 2 and 54,538 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 54,538 109,076
-1 -2 -54,538 -109,076

Now, we try dividing 109,076 by 3:

109,076 ÷ 3 = 36,358.6667

If the quotient is a whole number, then 3 and 36,358.6667 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 54,538 109,076
-1 -2 -54,538 -109,076

Let's try dividing by 4:

109,076 ÷ 4 = 27,269

If the quotient is a whole number, then 4 and 27,269 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 27,269 54,538 109,076
-1 -2 -4 -27,269 -54,538 109,076
Keep dividing by the next highest number until you cannot divide anymore.

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

1241122374467741341482684077378141,4741,6282,4792,9484,9589,91627,26954,538109,076
-1-2-4-11-22-37-44-67-74-134-148-268-407-737-814-1,474-1,628-2,479-2,948-4,958-9,916-27,269-54,538-109,076

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 109,076:


Ask a Question