Q: What are the factor combinations of the number 173,435?

 A:
Positive:   1 x 1734355 x 34687
Negative: -1 x -173435-5 x -34687


How do I find the factor combinations of the number 173,435?

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 173,435, 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.

1 173,435
-1 -173,435

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 173,435.

Example:
1 x 173,435 = 173,435
and
-1 x -173,435 = 173,435
Notice both answers equal 173,435

With that explanation out of the way, let's continue. Next, we take the number 173,435 and divide it by 2:

173,435 ÷ 2 = 86,717.5

If the quotient is a whole number, then 2 and 86,717.5 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:

1 173,435
-1 -173,435

Now, we try dividing 173,435 by 3:

173,435 ÷ 3 = 57,811.6667

If the quotient is a whole number, then 3 and 57,811.6667 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:

1 173,435
-1 -173,435

Let's try dividing by 4:

173,435 ÷ 4 = 43,358.75

If the quotient is a whole number, then 4 and 43,358.75 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:

1 173,435
-1 173,435
Keep dividing by the next highest number until you cannot divide anymore.

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

1534,687173,435
-1-5-34,687-173,435

More Examples

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