Q: What are the factor combinations of the number 338,978?

 A:
Positive:   1 x 3389782 x 169489
Negative: -1 x -338978-2 x -169489


How do I find the factor combinations of the number 338,978?

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 338,978, 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.

1 338,978
-1 -338,978

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 338,978.

Example:
1 x 338,978 = 338,978
and
-1 x -338,978 = 338,978
Notice both answers equal 338,978

With that explanation out of the way, let's continue. Next, we take the number 338,978 and divide it by 2:

338,978 ÷ 2 = 169,489

If the quotient is a whole number, then 2 and 169,489 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 2 169,489 338,978
-1 -2 -169,489 -338,978

Now, we try dividing 338,978 by 3:

338,978 ÷ 3 = 112,992.6667

If the quotient is a whole number, then 3 and 112,992.6667 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 2 169,489 338,978
-1 -2 -169,489 -338,978

Let's try dividing by 4:

338,978 ÷ 4 = 84,744.5

If the quotient is a whole number, then 4 and 84,744.5 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 2 169,489 338,978
-1 -2 -169,489 338,978
Keep dividing by the next highest number until you cannot divide anymore.

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

12169,489338,978
-1-2-169,489-338,978

More Examples

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