Q: What are the factor combinations of the number 17,329?

 A:
Positive:   1 x 1732913 x 133331 x 55943 x 403
Negative: -1 x -17329-13 x -1333-31 x -559-43 x -403


How do I find the factor combinations of the number 17,329?

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 17,329, 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 17,329
-1 -17,329

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 17,329.

Example:
1 x 17,329 = 17,329
and
-1 x -17,329 = 17,329
Notice both answers equal 17,329

With that explanation out of the way, let's continue. Next, we take the number 17,329 and divide it by 2:

17,329 ÷ 2 = 8,664.5

If the quotient is a whole number, then 2 and 8,664.5 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 17,329
-1 -17,329

Now, we try dividing 17,329 by 3:

17,329 ÷ 3 = 5,776.3333

If the quotient is a whole number, then 3 and 5,776.3333 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 17,329
-1 -17,329

Let's try dividing by 4:

17,329 ÷ 4 = 4,332.25

If the quotient is a whole number, then 4 and 4,332.25 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 17,329
-1 17,329
Keep dividing by the next highest number until you cannot divide anymore.

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

11331434035591,33317,329
-1-13-31-43-403-559-1,333-17,329

More Examples

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