Q: What are the factor combinations of the number 17,269?

 A:
Positive:   1 x 172697 x 2467
Negative: -1 x -17269-7 x -2467


How do I find the factor combinations of the number 17,269?

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 17,269, 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 17,269
-1 -17,269

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 17,269.

Example:
1 x 17,269 = 17,269
and
-1 x -17,269 = 17,269
Notice both answers equal 17,269

With that explanation out of the way, let's continue. Next, we take the number 17,269 and divide it by 2:

17,269 ÷ 2 = 8,634.5

If the quotient is a whole number, then 2 and 8,634.5 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 17,269
-1 -17,269

Now, we try dividing 17,269 by 3:

17,269 ÷ 3 = 5,756.3333

If the quotient is a whole number, then 3 and 5,756.3333 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 17,269
-1 -17,269

Let's try dividing by 4:

17,269 ÷ 4 = 4,317.25

If the quotient is a whole number, then 4 and 4,317.25 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 17,269
-1 17,269
Keep dividing by the next highest number until you cannot divide anymore.

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

172,46717,269
-1-7-2,467-17,269

More Examples

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