Q: What are the factor combinations of the number 313,031,303?

 A:
Positive:   1 x 31303130313 x 2407933153 x 590625167 x 4672109689 x 454327871 x 3593933551 x 881536781 x 46163
Negative: -1 x -313031303-13 x -24079331-53 x -5906251-67 x -4672109-689 x -454327-871 x -359393-3551 x -88153-6781 x -46163


How do I find the factor combinations of the number 313,031,303?

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 313,031,303, 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.

1 313,031,303
-1 -313,031,303

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 313,031,303.

Example:
1 x 313,031,303 = 313,031,303
and
-1 x -313,031,303 = 313,031,303
Notice both answers equal 313,031,303

With that explanation out of the way, let's continue. Next, we take the number 313,031,303 and divide it by 2:

313,031,303 ÷ 2 = 156,515,651.5

If the quotient is a whole number, then 2 and 156,515,651.5 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:

1 313,031,303
-1 -313,031,303

Now, we try dividing 313,031,303 by 3:

313,031,303 ÷ 3 = 104,343,767.6667

If the quotient is a whole number, then 3 and 104,343,767.6667 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:

1 313,031,303
-1 -313,031,303

Let's try dividing by 4:

313,031,303 ÷ 4 = 78,257,825.75

If the quotient is a whole number, then 4 and 78,257,825.75 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:

1 313,031,303
-1 313,031,303
Keep dividing by the next highest number until you cannot divide anymore.

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

11353676898713,5516,78146,16388,153359,393454,3274,672,1095,906,25124,079,331313,031,303
-1-13-53-67-689-871-3,551-6,781-46,163-88,153-359,393-454,327-4,672,109-5,906,251-24,079,331-313,031,303

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