Q: What are the factor combinations of the number 300,302,305?

 A:
Positive:   1 x 3003023055 x 6006046179 x 3801295239 x 1256495395 x 7602591195 x 2512993181 x 9440515905 x 18881
Negative: -1 x -300302305-5 x -60060461-79 x -3801295-239 x -1256495-395 x -760259-1195 x -251299-3181 x -94405-15905 x -18881


How do I find the factor combinations of the number 300,302,305?

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 300,302,305, 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.

1 300,302,305
-1 -300,302,305

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 300,302,305.

Example:
1 x 300,302,305 = 300,302,305
and
-1 x -300,302,305 = 300,302,305
Notice both answers equal 300,302,305

With that explanation out of the way, let's continue. Next, we take the number 300,302,305 and divide it by 2:

300,302,305 ÷ 2 = 150,151,152.5

If the quotient is a whole number, then 2 and 150,151,152.5 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:

1 300,302,305
-1 -300,302,305

Now, we try dividing 300,302,305 by 3:

300,302,305 ÷ 3 = 100,100,768.3333

If the quotient is a whole number, then 3 and 100,100,768.3333 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:

1 300,302,305
-1 -300,302,305

Let's try dividing by 4:

300,302,305 ÷ 4 = 75,075,576.25

If the quotient is a whole number, then 4 and 75,075,576.25 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:

1 300,302,305
-1 300,302,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15792393951,1953,18115,90518,88194,405251,299760,2591,256,4953,801,29560,060,461300,302,305
-1-5-79-239-395-1,195-3,181-15,905-18,881-94,405-251,299-760,259-1,256,495-3,801,295-60,060,461-300,302,305

More Examples

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