Q: What are the factor combinations of the number 303,120,415?

 A:
Positive:   1 x 3031204155 x 6062408313 x 2331695565 x 46633912113 x 1434552207 x 13734510565 x 2869111035 x 27469
Negative: -1 x -303120415-5 x -60624083-13 x -23316955-65 x -4663391-2113 x -143455-2207 x -137345-10565 x -28691-11035 x -27469


How do I find the factor combinations of the number 303,120,415?

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 303,120,415, 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.

1 303,120,415
-1 -303,120,415

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 303,120,415.

Example:
1 x 303,120,415 = 303,120,415
and
-1 x -303,120,415 = 303,120,415
Notice both answers equal 303,120,415

With that explanation out of the way, let's continue. Next, we take the number 303,120,415 and divide it by 2:

303,120,415 ÷ 2 = 151,560,207.5

If the quotient is a whole number, then 2 and 151,560,207.5 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:

1 303,120,415
-1 -303,120,415

Now, we try dividing 303,120,415 by 3:

303,120,415 ÷ 3 = 101,040,138.3333

If the quotient is a whole number, then 3 and 101,040,138.3333 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:

1 303,120,415
-1 -303,120,415

Let's try dividing by 4:

303,120,415 ÷ 4 = 75,780,103.75

If the quotient is a whole number, then 4 and 75,780,103.75 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:

1 303,120,415
-1 303,120,415
Keep dividing by the next highest number until you cannot divide anymore.

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

1513652,1132,20710,56511,03527,46928,691137,345143,4554,663,39123,316,95560,624,083303,120,415
-1-5-13-65-2,113-2,207-10,565-11,035-27,469-28,691-137,345-143,455-4,663,391-23,316,955-60,624,083-303,120,415

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