Q: What are the factor combinations of the number 3,123,239?

 A:
Positive:   1 x 31232397 x 44617719 x 16438123 x 135793133 x 23483161 x 19399437 x 71471021 x 3059
Negative: -1 x -3123239-7 x -446177-19 x -164381-23 x -135793-133 x -23483-161 x -19399-437 x -7147-1021 x -3059


How do I find the factor combinations of the number 3,123,239?

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 3,123,239, 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 3,123,239
-1 -3,123,239

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 3,123,239.

Example:
1 x 3,123,239 = 3,123,239
and
-1 x -3,123,239 = 3,123,239
Notice both answers equal 3,123,239

With that explanation out of the way, let's continue. Next, we take the number 3,123,239 and divide it by 2:

3,123,239 ÷ 2 = 1,561,619.5

If the quotient is a whole number, then 2 and 1,561,619.5 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 3,123,239
-1 -3,123,239

Now, we try dividing 3,123,239 by 3:

3,123,239 ÷ 3 = 1,041,079.6667

If the quotient is a whole number, then 3 and 1,041,079.6667 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 3,123,239
-1 -3,123,239

Let's try dividing by 4:

3,123,239 ÷ 4 = 780,809.75

If the quotient is a whole number, then 4 and 780,809.75 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 3,123,239
-1 3,123,239
Keep dividing by the next highest number until you cannot divide anymore.

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

1719231331614371,0213,0597,14719,39923,483135,793164,381446,1773,123,239
-1-7-19-23-133-161-437-1,021-3,059-7,147-19,399-23,483-135,793-164,381-446,177-3,123,239

More Examples

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