Q: What are the factor combinations of the number 303,123,515?

 A:
Positive:   1 x 3031235155 x 6062470317 x 1783079529 x 1045253585 x 3566159145 x 2090507493 x 6148552465 x 122971
Negative: -1 x -303123515-5 x -60624703-17 x -17830795-29 x -10452535-85 x -3566159-145 x -2090507-493 x -614855-2465 x -122971


How do I find the factor combinations of the number 303,123,515?

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 303,123,515, 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.

1 303,123,515
-1 -303,123,515

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 303,123,515.

Example:
1 x 303,123,515 = 303,123,515
and
-1 x -303,123,515 = 303,123,515
Notice both answers equal 303,123,515

With that explanation out of the way, let's continue. Next, we take the number 303,123,515 and divide it by 2:

303,123,515 ÷ 2 = 151,561,757.5

If the quotient is a whole number, then 2 and 151,561,757.5 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:

1 303,123,515
-1 -303,123,515

Now, we try dividing 303,123,515 by 3:

303,123,515 ÷ 3 = 101,041,171.6667

If the quotient is a whole number, then 3 and 101,041,171.6667 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:

1 303,123,515
-1 -303,123,515

Let's try dividing by 4:

303,123,515 ÷ 4 = 75,780,878.75

If the quotient is a whole number, then 4 and 75,780,878.75 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:

1 303,123,515
-1 303,123,515
Keep dividing by the next highest number until you cannot divide anymore.

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

151729851454932,465122,971614,8552,090,5073,566,15910,452,53517,830,79560,624,703303,123,515
-1-5-17-29-85-145-493-2,465-122,971-614,855-2,090,507-3,566,159-10,452,535-17,830,795-60,624,703-303,123,515

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