Q: What are the factor combinations of the number 172,783?

 A:
Positive:   1 x 17278313 x 13291
Negative: -1 x -172783-13 x -13291


How do I find the factor combinations of the number 172,783?

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 172,783, 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.

1 172,783
-1 -172,783

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 172,783.

Example:
1 x 172,783 = 172,783
and
-1 x -172,783 = 172,783
Notice both answers equal 172,783

With that explanation out of the way, let's continue. Next, we take the number 172,783 and divide it by 2:

172,783 ÷ 2 = 86,391.5

If the quotient is a whole number, then 2 and 86,391.5 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:

1 172,783
-1 -172,783

Now, we try dividing 172,783 by 3:

172,783 ÷ 3 = 57,594.3333

If the quotient is a whole number, then 3 and 57,594.3333 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:

1 172,783
-1 -172,783

Let's try dividing by 4:

172,783 ÷ 4 = 43,195.75

If the quotient is a whole number, then 4 and 43,195.75 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:

1 172,783
-1 172,783
Keep dividing by the next highest number until you cannot divide anymore.

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

11313,291172,783
-1-13-13,291-172,783

More Examples

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