Q: What are the factor combinations of the number 300,521,035?

 A:
Positive:   1 x 3005210355 x 6010420797 x 3098155485 x 619631601 x 5000351031 x 2914853005 x 1000075155 x 58297
Negative: -1 x -300521035-5 x -60104207-97 x -3098155-485 x -619631-601 x -500035-1031 x -291485-3005 x -100007-5155 x -58297


How do I find the factor combinations of the number 300,521,035?

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 300,521,035, 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.

1 300,521,035
-1 -300,521,035

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 300,521,035.

Example:
1 x 300,521,035 = 300,521,035
and
-1 x -300,521,035 = 300,521,035
Notice both answers equal 300,521,035

With that explanation out of the way, let's continue. Next, we take the number 300,521,035 and divide it by 2:

300,521,035 ÷ 2 = 150,260,517.5

If the quotient is a whole number, then 2 and 150,260,517.5 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:

1 300,521,035
-1 -300,521,035

Now, we try dividing 300,521,035 by 3:

300,521,035 ÷ 3 = 100,173,678.3333

If the quotient is a whole number, then 3 and 100,173,678.3333 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:

1 300,521,035
-1 -300,521,035

Let's try dividing by 4:

300,521,035 ÷ 4 = 75,130,258.75

If the quotient is a whole number, then 4 and 75,130,258.75 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:

1 300,521,035
-1 300,521,035
Keep dividing by the next highest number until you cannot divide anymore.

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

15974856011,0313,0055,15558,297100,007291,485500,035619,6313,098,15560,104,207300,521,035
-1-5-97-485-601-1,031-3,005-5,155-58,297-100,007-291,485-500,035-619,631-3,098,155-60,104,207-300,521,035

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