Q: What are the factor combinations of the number 304,322,405?

 A:
Positive:   1 x 3043224055 x 6086448183 x 3666535415 x 733307
Negative: -1 x -304322405-5 x -60864481-83 x -3666535-415 x -733307


How do I find the factor combinations of the number 304,322,405?

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 304,322,405, 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.

1 304,322,405
-1 -304,322,405

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 304,322,405.

Example:
1 x 304,322,405 = 304,322,405
and
-1 x -304,322,405 = 304,322,405
Notice both answers equal 304,322,405

With that explanation out of the way, let's continue. Next, we take the number 304,322,405 and divide it by 2:

304,322,405 ÷ 2 = 152,161,202.5

If the quotient is a whole number, then 2 and 152,161,202.5 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:

1 304,322,405
-1 -304,322,405

Now, we try dividing 304,322,405 by 3:

304,322,405 ÷ 3 = 101,440,801.6667

If the quotient is a whole number, then 3 and 101,440,801.6667 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:

1 304,322,405
-1 -304,322,405

Let's try dividing by 4:

304,322,405 ÷ 4 = 76,080,601.25

If the quotient is a whole number, then 4 and 76,080,601.25 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:

1 304,322,405
-1 304,322,405
Keep dividing by the next highest number until you cannot divide anymore.

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

1583415733,3073,666,53560,864,481304,322,405
-1-5-83-415-733,307-3,666,535-60,864,481-304,322,405

More Examples

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