Q: What are the factor combinations of the number 598,917?

 A:
Positive:   1 x 5989173 x 19963911 x 5444733 x 18149
Negative: -1 x -598917-3 x -199639-11 x -54447-33 x -18149


How do I find the factor combinations of the number 598,917?

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 598,917, 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.

1 598,917
-1 -598,917

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 598,917.

Example:
1 x 598,917 = 598,917
and
-1 x -598,917 = 598,917
Notice both answers equal 598,917

With that explanation out of the way, let's continue. Next, we take the number 598,917 and divide it by 2:

598,917 ÷ 2 = 299,458.5

If the quotient is a whole number, then 2 and 299,458.5 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:

1 598,917
-1 -598,917

Now, we try dividing 598,917 by 3:

598,917 ÷ 3 = 199,639

If the quotient is a whole number, then 3 and 199,639 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 3 199,639 598,917
-1 -3 -199,639 -598,917

Let's try dividing by 4:

598,917 ÷ 4 = 149,729.25

If the quotient is a whole number, then 4 and 149,729.25 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 3 199,639 598,917
-1 -3 -199,639 598,917
Keep dividing by the next highest number until you cannot divide anymore.

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

13113318,14954,447199,639598,917
-1-3-11-33-18,149-54,447-199,639-598,917

More Examples

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