Q: What are the factor combinations of the number 304,310,539?

 A:
Positive:   1 x 30431053913 x 2340850323 x 1323089331 x 9816469299 x 1017761403 x 755113713 x 4268039269 x 32831
Negative: -1 x -304310539-13 x -23408503-23 x -13230893-31 x -9816469-299 x -1017761-403 x -755113-713 x -426803-9269 x -32831


How do I find the factor combinations of the number 304,310,539?

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 304,310,539, 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.

1 304,310,539
-1 -304,310,539

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 304,310,539.

Example:
1 x 304,310,539 = 304,310,539
and
-1 x -304,310,539 = 304,310,539
Notice both answers equal 304,310,539

With that explanation out of the way, let's continue. Next, we take the number 304,310,539 and divide it by 2:

304,310,539 ÷ 2 = 152,155,269.5

If the quotient is a whole number, then 2 and 152,155,269.5 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:

1 304,310,539
-1 -304,310,539

Now, we try dividing 304,310,539 by 3:

304,310,539 ÷ 3 = 101,436,846.3333

If the quotient is a whole number, then 3 and 101,436,846.3333 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:

1 304,310,539
-1 -304,310,539

Let's try dividing by 4:

304,310,539 ÷ 4 = 76,077,634.75

If the quotient is a whole number, then 4 and 76,077,634.75 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:

1 304,310,539
-1 304,310,539
Keep dividing by the next highest number until you cannot divide anymore.

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

11323312994037139,26932,831426,803755,1131,017,7619,816,46913,230,89323,408,503304,310,539
-1-13-23-31-299-403-713-9,269-32,831-426,803-755,113-1,017,761-9,816,469-13,230,893-23,408,503-304,310,539

More Examples

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