Q: What are the factor combinations of the number 728,999?

 A:
Positive:   1 x 72899989 x 8191
Negative: -1 x -728999-89 x -8191


How do I find the factor combinations of the number 728,999?

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 728,999, 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.

1 728,999
-1 -728,999

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 728,999.

Example:
1 x 728,999 = 728,999
and
-1 x -728,999 = 728,999
Notice both answers equal 728,999

With that explanation out of the way, let's continue. Next, we take the number 728,999 and divide it by 2:

728,999 ÷ 2 = 364,499.5

If the quotient is a whole number, then 2 and 364,499.5 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:

1 728,999
-1 -728,999

Now, we try dividing 728,999 by 3:

728,999 ÷ 3 = 242,999.6667

If the quotient is a whole number, then 3 and 242,999.6667 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:

1 728,999
-1 -728,999

Let's try dividing by 4:

728,999 ÷ 4 = 182,249.75

If the quotient is a whole number, then 4 and 182,249.75 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:

1 728,999
-1 728,999
Keep dividing by the next highest number until you cannot divide anymore.

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

1898,191728,999
-1-89-8,191-728,999

More Examples

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