Q: What are the factor combinations of the number 106,913?

 A:
Positive:   1 x 10691317 x 628919 x 5627323 x 331
Negative: -1 x -106913-17 x -6289-19 x -5627-323 x -331


How do I find the factor combinations of the number 106,913?

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 106,913, 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.

1 106,913
-1 -106,913

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 106,913.

Example:
1 x 106,913 = 106,913
and
-1 x -106,913 = 106,913
Notice both answers equal 106,913

With that explanation out of the way, let's continue. Next, we take the number 106,913 and divide it by 2:

106,913 ÷ 2 = 53,456.5

If the quotient is a whole number, then 2 and 53,456.5 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:

1 106,913
-1 -106,913

Now, we try dividing 106,913 by 3:

106,913 ÷ 3 = 35,637.6667

If the quotient is a whole number, then 3 and 35,637.6667 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:

1 106,913
-1 -106,913

Let's try dividing by 4:

106,913 ÷ 4 = 26,728.25

If the quotient is a whole number, then 4 and 26,728.25 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:

1 106,913
-1 106,913
Keep dividing by the next highest number until you cannot divide anymore.

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

117193233315,6276,289106,913
-1-17-19-323-331-5,627-6,289-106,913

More Examples

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