Q: What are the factor combinations of the number 107,538?

 A:
Positive:   1 x 1075382 x 537693 x 358466 x 17923
Negative: -1 x -107538-2 x -53769-3 x -35846-6 x -17923


How do I find the factor combinations of the number 107,538?

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 107,538, 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.

1 107,538
-1 -107,538

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 107,538.

Example:
1 x 107,538 = 107,538
and
-1 x -107,538 = 107,538
Notice both answers equal 107,538

With that explanation out of the way, let's continue. Next, we take the number 107,538 and divide it by 2:

107,538 ÷ 2 = 53,769

If the quotient is a whole number, then 2 and 53,769 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 53,769 107,538
-1 -2 -53,769 -107,538

Now, we try dividing 107,538 by 3:

107,538 ÷ 3 = 35,846

If the quotient is a whole number, then 3 and 35,846 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 35,846 53,769 107,538
-1 -2 -3 -35,846 -53,769 -107,538

Let's try dividing by 4:

107,538 ÷ 4 = 26,884.5

If the quotient is a whole number, then 4 and 26,884.5 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 35,846 53,769 107,538
-1 -2 -3 -35,846 -53,769 107,538
Keep dividing by the next highest number until you cannot divide anymore.

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

123617,92335,84653,769107,538
-1-2-3-6-17,923-35,846-53,769-107,538

More Examples

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