Q: What are the factor combinations of the number 17,017?

 A:
Positive:   1 x 170177 x 243111 x 154713 x 130917 x 100177 x 22191 x 187119 x 143
Negative: -1 x -17017-7 x -2431-11 x -1547-13 x -1309-17 x -1001-77 x -221-91 x -187-119 x -143


How do I find the factor combinations of the number 17,017?

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 17,017, 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 17,017
-1 -17,017

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 17,017.

Example:
1 x 17,017 = 17,017
and
-1 x -17,017 = 17,017
Notice both answers equal 17,017

With that explanation out of the way, let's continue. Next, we take the number 17,017 and divide it by 2:

17,017 ÷ 2 = 8,508.5

If the quotient is a whole number, then 2 and 8,508.5 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 17,017
-1 -17,017

Now, we try dividing 17,017 by 3:

17,017 ÷ 3 = 5,672.3333

If the quotient is a whole number, then 3 and 5,672.3333 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 17,017
-1 -17,017

Let's try dividing by 4:

17,017 ÷ 4 = 4,254.25

If the quotient is a whole number, then 4 and 4,254.25 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 17,017
-1 17,017
Keep dividing by the next highest number until you cannot divide anymore.

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

1711131777911191431872211,0011,3091,5472,43117,017
-1-7-11-13-17-77-91-119-143-187-221-1,001-1,309-1,547-2,431-17,017

More Examples

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