Q: What are the factor combinations of the number 711,623?

 A:
Positive:   1 x 71162311 x 64693
Negative: -1 x -711623-11 x -64693


How do I find the factor combinations of the number 711,623?

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 711,623, 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.

1 711,623
-1 -711,623

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 711,623.

Example:
1 x 711,623 = 711,623
and
-1 x -711,623 = 711,623
Notice both answers equal 711,623

With that explanation out of the way, let's continue. Next, we take the number 711,623 and divide it by 2:

711,623 ÷ 2 = 355,811.5

If the quotient is a whole number, then 2 and 355,811.5 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:

1 711,623
-1 -711,623

Now, we try dividing 711,623 by 3:

711,623 ÷ 3 = 237,207.6667

If the quotient is a whole number, then 3 and 237,207.6667 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:

1 711,623
-1 -711,623

Let's try dividing by 4:

711,623 ÷ 4 = 177,905.75

If the quotient is a whole number, then 4 and 177,905.75 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:

1 711,623
-1 711,623
Keep dividing by the next highest number until you cannot divide anymore.

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

11164,693711,623
-1-11-64,693-711,623

More Examples

Here are some more numbers to try:

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