Q: What are the factor combinations of the number 707,713?

 A:
Positive:   1 x 707713103 x 6871
Negative: -1 x -707713-103 x -6871


How do I find the factor combinations of the number 707,713?

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 707,713, 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.

1 707,713
-1 -707,713

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 707,713.

Example:
1 x 707,713 = 707,713
and
-1 x -707,713 = 707,713
Notice both answers equal 707,713

With that explanation out of the way, let's continue. Next, we take the number 707,713 and divide it by 2:

707,713 ÷ 2 = 353,856.5

If the quotient is a whole number, then 2 and 353,856.5 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:

1 707,713
-1 -707,713

Now, we try dividing 707,713 by 3:

707,713 ÷ 3 = 235,904.3333

If the quotient is a whole number, then 3 and 235,904.3333 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:

1 707,713
-1 -707,713

Let's try dividing by 4:

707,713 ÷ 4 = 176,928.25

If the quotient is a whole number, then 4 and 176,928.25 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:

1 707,713
-1 707,713
Keep dividing by the next highest number until you cannot divide anymore.

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

11036,871707,713
-1-103-6,871-707,713

More Examples

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