Q: What are the factor combinations of the number 685,259?

 A:
Positive:   1 x 685259103 x 6653
Negative: -1 x -685259-103 x -6653


How do I find the factor combinations of the number 685,259?

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 685,259, 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.

1 685,259
-1 -685,259

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 685,259.

Example:
1 x 685,259 = 685,259
and
-1 x -685,259 = 685,259
Notice both answers equal 685,259

With that explanation out of the way, let's continue. Next, we take the number 685,259 and divide it by 2:

685,259 ÷ 2 = 342,629.5

If the quotient is a whole number, then 2 and 342,629.5 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:

1 685,259
-1 -685,259

Now, we try dividing 685,259 by 3:

685,259 ÷ 3 = 228,419.6667

If the quotient is a whole number, then 3 and 228,419.6667 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:

1 685,259
-1 -685,259

Let's try dividing by 4:

685,259 ÷ 4 = 171,314.75

If the quotient is a whole number, then 4 and 171,314.75 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:

1 685,259
-1 685,259
Keep dividing by the next highest number until you cannot divide anymore.

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

11036,653685,259
-1-103-6,653-685,259

More Examples

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