Q: What are the factor combinations of the number 300,003,221?

 A:
Positive:   1 x 3000032217 x 428576031987 x 15098313909 x 21569
Negative: -1 x -300003221-7 x -42857603-1987 x -150983-13909 x -21569


How do I find the factor combinations of the number 300,003,221?

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 300,003,221, 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.

1 300,003,221
-1 -300,003,221

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 300,003,221.

Example:
1 x 300,003,221 = 300,003,221
and
-1 x -300,003,221 = 300,003,221
Notice both answers equal 300,003,221

With that explanation out of the way, let's continue. Next, we take the number 300,003,221 and divide it by 2:

300,003,221 ÷ 2 = 150,001,610.5

If the quotient is a whole number, then 2 and 150,001,610.5 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:

1 300,003,221
-1 -300,003,221

Now, we try dividing 300,003,221 by 3:

300,003,221 ÷ 3 = 100,001,073.6667

If the quotient is a whole number, then 3 and 100,001,073.6667 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:

1 300,003,221
-1 -300,003,221

Let's try dividing by 4:

300,003,221 ÷ 4 = 75,000,805.25

If the quotient is a whole number, then 4 and 75,000,805.25 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:

1 300,003,221
-1 300,003,221
Keep dividing by the next highest number until you cannot divide anymore.

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

171,98713,90921,569150,98342,857,603300,003,221
-1-7-1,987-13,909-21,569-150,983-42,857,603-300,003,221

More Examples

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