Q: What are the factor combinations of the number 304,054,864?

 A:
Positive:   1 x 3040548642 x 1520274324 x 760137168 x 3800685816 x 19003429
Negative: -1 x -304054864-2 x -152027432-4 x -76013716-8 x -38006858-16 x -19003429


How do I find the factor combinations of the number 304,054,864?

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 304,054,864, 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.

1 304,054,864
-1 -304,054,864

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 304,054,864.

Example:
1 x 304,054,864 = 304,054,864
and
-1 x -304,054,864 = 304,054,864
Notice both answers equal 304,054,864

With that explanation out of the way, let's continue. Next, we take the number 304,054,864 and divide it by 2:

304,054,864 ÷ 2 = 152,027,432

If the quotient is a whole number, then 2 and 152,027,432 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 152,027,432 304,054,864
-1 -2 -152,027,432 -304,054,864

Now, we try dividing 304,054,864 by 3:

304,054,864 ÷ 3 = 101,351,621.3333

If the quotient is a whole number, then 3 and 101,351,621.3333 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 2 152,027,432 304,054,864
-1 -2 -152,027,432 -304,054,864

Let's try dividing by 4:

304,054,864 ÷ 4 = 76,013,716

If the quotient is a whole number, then 4 and 76,013,716 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 76,013,716 152,027,432 304,054,864
-1 -2 -4 -76,013,716 -152,027,432 304,054,864
Keep dividing by the next highest number until you cannot divide anymore.

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

12481619,003,42938,006,85876,013,716152,027,432304,054,864
-1-2-4-8-16-19,003,429-38,006,858-76,013,716-152,027,432-304,054,864

More Examples

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