Q: What are the factor combinations of the number 330,300,305?

 A:
Positive:   1 x 3303003055 x 6606006141 x 8056105205 x 1611221863 x 3827351867 x 1769154315 x 765479335 x 35383
Negative: -1 x -330300305-5 x -66060061-41 x -8056105-205 x -1611221-863 x -382735-1867 x -176915-4315 x -76547-9335 x -35383


How do I find the factor combinations of the number 330,300,305?

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 330,300,305, 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.

1 330,300,305
-1 -330,300,305

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 330,300,305.

Example:
1 x 330,300,305 = 330,300,305
and
-1 x -330,300,305 = 330,300,305
Notice both answers equal 330,300,305

With that explanation out of the way, let's continue. Next, we take the number 330,300,305 and divide it by 2:

330,300,305 ÷ 2 = 165,150,152.5

If the quotient is a whole number, then 2 and 165,150,152.5 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:

1 330,300,305
-1 -330,300,305

Now, we try dividing 330,300,305 by 3:

330,300,305 ÷ 3 = 110,100,101.6667

If the quotient is a whole number, then 3 and 110,100,101.6667 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:

1 330,300,305
-1 -330,300,305

Let's try dividing by 4:

330,300,305 ÷ 4 = 82,575,076.25

If the quotient is a whole number, then 4 and 82,575,076.25 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:

1 330,300,305
-1 330,300,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15412058631,8674,3159,33535,38376,547176,915382,7351,611,2218,056,10566,060,061330,300,305
-1-5-41-205-863-1,867-4,315-9,335-35,383-76,547-176,915-382,735-1,611,221-8,056,105-66,060,061-330,300,305

More Examples

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