Q: What are the factor combinations of the number 300,213,667?

 A:
Positive:   1 x 30021366713 x 2309335967 x 448080179 x 3800173871 x 3446771027 x 2923214363 x 688095293 x 56719
Negative: -1 x -300213667-13 x -23093359-67 x -4480801-79 x -3800173-871 x -344677-1027 x -292321-4363 x -68809-5293 x -56719


How do I find the factor combinations of the number 300,213,667?

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 300,213,667, 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.

1 300,213,667
-1 -300,213,667

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 300,213,667.

Example:
1 x 300,213,667 = 300,213,667
and
-1 x -300,213,667 = 300,213,667
Notice both answers equal 300,213,667

With that explanation out of the way, let's continue. Next, we take the number 300,213,667 and divide it by 2:

300,213,667 ÷ 2 = 150,106,833.5

If the quotient is a whole number, then 2 and 150,106,833.5 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:

1 300,213,667
-1 -300,213,667

Now, we try dividing 300,213,667 by 3:

300,213,667 ÷ 3 = 100,071,222.3333

If the quotient is a whole number, then 3 and 100,071,222.3333 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:

1 300,213,667
-1 -300,213,667

Let's try dividing by 4:

300,213,667 ÷ 4 = 75,053,416.75

If the quotient is a whole number, then 4 and 75,053,416.75 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:

1 300,213,667
-1 300,213,667
Keep dividing by the next highest number until you cannot divide anymore.

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

11367798711,0274,3635,29356,71968,809292,321344,6773,800,1734,480,80123,093,359300,213,667
-1-13-67-79-871-1,027-4,363-5,293-56,719-68,809-292,321-344,677-3,800,173-4,480,801-23,093,359-300,213,667

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