Q: What are the factor combinations of the number 709,805?

 A:
Positive:   1 x 7098055 x 141961
Negative: -1 x -709805-5 x -141961


How do I find the factor combinations of the number 709,805?

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 709,805, 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.

1 709,805
-1 -709,805

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 709,805.

Example:
1 x 709,805 = 709,805
and
-1 x -709,805 = 709,805
Notice both answers equal 709,805

With that explanation out of the way, let's continue. Next, we take the number 709,805 and divide it by 2:

709,805 ÷ 2 = 354,902.5

If the quotient is a whole number, then 2 and 354,902.5 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:

1 709,805
-1 -709,805

Now, we try dividing 709,805 by 3:

709,805 ÷ 3 = 236,601.6667

If the quotient is a whole number, then 3 and 236,601.6667 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:

1 709,805
-1 -709,805

Let's try dividing by 4:

709,805 ÷ 4 = 177,451.25

If the quotient is a whole number, then 4 and 177,451.25 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:

1 709,805
-1 709,805
Keep dividing by the next highest number until you cannot divide anymore.

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

15141,961709,805
-1-5-141,961-709,805

More Examples

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