Q: What are the factor combinations of the number 311,002,223?

 A:
Positive:   1 x 3110022237 x 4442888971 x 438031379 x 393673789 x 3494407497 x 625759553 x 562391623 x 4992015609 x 554476319 x 492177031 x 442337921 x 39263
Negative: -1 x -311002223-7 x -44428889-71 x -4380313-79 x -3936737-89 x -3494407-497 x -625759-553 x -562391-623 x -499201-5609 x -55447-6319 x -49217-7031 x -44233-7921 x -39263


How do I find the factor combinations of the number 311,002,223?

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 311,002,223, 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.

1 311,002,223
-1 -311,002,223

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 311,002,223.

Example:
1 x 311,002,223 = 311,002,223
and
-1 x -311,002,223 = 311,002,223
Notice both answers equal 311,002,223

With that explanation out of the way, let's continue. Next, we take the number 311,002,223 and divide it by 2:

311,002,223 ÷ 2 = 155,501,111.5

If the quotient is a whole number, then 2 and 155,501,111.5 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:

1 311,002,223
-1 -311,002,223

Now, we try dividing 311,002,223 by 3:

311,002,223 ÷ 3 = 103,667,407.6667

If the quotient is a whole number, then 3 and 103,667,407.6667 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:

1 311,002,223
-1 -311,002,223

Let's try dividing by 4:

311,002,223 ÷ 4 = 77,750,555.75

If the quotient is a whole number, then 4 and 77,750,555.75 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:

1 311,002,223
-1 311,002,223
Keep dividing by the next highest number until you cannot divide anymore.

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

177179894975536235,6096,3197,0317,92139,26344,23349,21755,447499,201562,391625,7593,494,4073,936,7374,380,31344,428,889311,002,223
-1-7-71-79-89-497-553-623-5,609-6,319-7,031-7,921-39,263-44,233-49,217-55,447-499,201-562,391-625,759-3,494,407-3,936,737-4,380,313-44,428,889-311,002,223

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