Q: What are the factor combinations of the number 522,993?

 A:
Positive:   1 x 5229933 x 174331
Negative: -1 x -522993-3 x -174331


How do I find the factor combinations of the number 522,993?

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 522,993, 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.

1 522,993
-1 -522,993

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 522,993.

Example:
1 x 522,993 = 522,993
and
-1 x -522,993 = 522,993
Notice both answers equal 522,993

With that explanation out of the way, let's continue. Next, we take the number 522,993 and divide it by 2:

522,993 ÷ 2 = 261,496.5

If the quotient is a whole number, then 2 and 261,496.5 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:

1 522,993
-1 -522,993

Now, we try dividing 522,993 by 3:

522,993 ÷ 3 = 174,331

If the quotient is a whole number, then 3 and 174,331 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 3 174,331 522,993
-1 -3 -174,331 -522,993

Let's try dividing by 4:

522,993 ÷ 4 = 130,748.25

If the quotient is a whole number, then 4 and 130,748.25 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 3 174,331 522,993
-1 -3 -174,331 522,993
Keep dividing by the next highest number until you cannot divide anymore.

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

13174,331522,993
-1-3-174,331-522,993

More Examples

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