Q: What are the factor combinations of the number 300,131,321?

 A:
Positive:   1 x 3001313217 x 4287590349 x 6125129421 x 7129012947 x 10184314549 x 20629
Negative: -1 x -300131321-7 x -42875903-49 x -6125129-421 x -712901-2947 x -101843-14549 x -20629


How do I find the factor combinations of the number 300,131,321?

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 300,131,321, 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.

1 300,131,321
-1 -300,131,321

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 300,131,321.

Example:
1 x 300,131,321 = 300,131,321
and
-1 x -300,131,321 = 300,131,321
Notice both answers equal 300,131,321

With that explanation out of the way, let's continue. Next, we take the number 300,131,321 and divide it by 2:

300,131,321 ÷ 2 = 150,065,660.5

If the quotient is a whole number, then 2 and 150,065,660.5 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:

1 300,131,321
-1 -300,131,321

Now, we try dividing 300,131,321 by 3:

300,131,321 ÷ 3 = 100,043,773.6667

If the quotient is a whole number, then 3 and 100,043,773.6667 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:

1 300,131,321
-1 -300,131,321

Let's try dividing by 4:

300,131,321 ÷ 4 = 75,032,830.25

If the quotient is a whole number, then 4 and 75,032,830.25 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:

1 300,131,321
-1 300,131,321
Keep dividing by the next highest number until you cannot divide anymore.

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

17494212,94714,54920,629101,843712,9016,125,12942,875,903300,131,321
-1-7-49-421-2,947-14,549-20,629-101,843-712,901-6,125,129-42,875,903-300,131,321

More Examples

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