Q: What are the factor combinations of the number 172,167?

 A:
Positive:   1 x 1721673 x 57389
Negative: -1 x -172167-3 x -57389


How do I find the factor combinations of the number 172,167?

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 172,167, 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.

1 172,167
-1 -172,167

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 172,167.

Example:
1 x 172,167 = 172,167
and
-1 x -172,167 = 172,167
Notice both answers equal 172,167

With that explanation out of the way, let's continue. Next, we take the number 172,167 and divide it by 2:

172,167 ÷ 2 = 86,083.5

If the quotient is a whole number, then 2 and 86,083.5 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:

1 172,167
-1 -172,167

Now, we try dividing 172,167 by 3:

172,167 ÷ 3 = 57,389

If the quotient is a whole number, then 3 and 57,389 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 57,389 172,167
-1 -3 -57,389 -172,167

Let's try dividing by 4:

172,167 ÷ 4 = 43,041.75

If the quotient is a whole number, then 4 and 43,041.75 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 3 57,389 172,167
-1 -3 -57,389 172,167
Keep dividing by the next highest number until you cannot divide anymore.

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

1357,389172,167
-1-3-57,389-172,167

More Examples

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