Q: What are the factor combinations of the number 711,949?

 A:
Positive:   1 x 7119497 x 10170719 x 3747153 x 13433101 x 7049133 x 5353371 x 1919707 x 1007
Negative: -1 x -711949-7 x -101707-19 x -37471-53 x -13433-101 x -7049-133 x -5353-371 x -1919-707 x -1007


How do I find the factor combinations of the number 711,949?

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 711,949, 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.

1 711,949
-1 -711,949

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 711,949.

Example:
1 x 711,949 = 711,949
and
-1 x -711,949 = 711,949
Notice both answers equal 711,949

With that explanation out of the way, let's continue. Next, we take the number 711,949 and divide it by 2:

711,949 ÷ 2 = 355,974.5

If the quotient is a whole number, then 2 and 355,974.5 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:

1 711,949
-1 -711,949

Now, we try dividing 711,949 by 3:

711,949 ÷ 3 = 237,316.3333

If the quotient is a whole number, then 3 and 237,316.3333 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:

1 711,949
-1 -711,949

Let's try dividing by 4:

711,949 ÷ 4 = 177,987.25

If the quotient is a whole number, then 4 and 177,987.25 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:

1 711,949
-1 711,949
Keep dividing by the next highest number until you cannot divide anymore.

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

1719531011333717071,0071,9195,3537,04913,43337,471101,707711,949
-1-7-19-53-101-133-371-707-1,007-1,919-5,353-7,049-13,433-37,471-101,707-711,949

More Examples

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