Q: What are the factor combinations of the number 330,000,301?

 A:
Positive:   1 x 33000030131 x 1064517147 x 702128361 x 540984179 x 41772191457 x 2264931891 x 1745112209 x 1493892449 x 1347492867 x 1151033713 x 888774819 x 68479
Negative: -1 x -330000301-31 x -10645171-47 x -7021283-61 x -5409841-79 x -4177219-1457 x -226493-1891 x -174511-2209 x -149389-2449 x -134749-2867 x -115103-3713 x -88877-4819 x -68479


How do I find the factor combinations of the number 330,000,301?

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 330,000,301, 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.

1 330,000,301
-1 -330,000,301

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 330,000,301.

Example:
1 x 330,000,301 = 330,000,301
and
-1 x -330,000,301 = 330,000,301
Notice both answers equal 330,000,301

With that explanation out of the way, let's continue. Next, we take the number 330,000,301 and divide it by 2:

330,000,301 ÷ 2 = 165,000,150.5

If the quotient is a whole number, then 2 and 165,000,150.5 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:

1 330,000,301
-1 -330,000,301

Now, we try dividing 330,000,301 by 3:

330,000,301 ÷ 3 = 110,000,100.3333

If the quotient is a whole number, then 3 and 110,000,100.3333 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:

1 330,000,301
-1 -330,000,301

Let's try dividing by 4:

330,000,301 ÷ 4 = 82,500,075.25

If the quotient is a whole number, then 4 and 82,500,075.25 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:

1 330,000,301
-1 330,000,301
Keep dividing by the next highest number until you cannot divide anymore.

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

1314761791,4571,8912,2092,4492,8673,7134,81968,47988,877115,103134,749149,389174,511226,4934,177,2195,409,8417,021,28310,645,171330,000,301
-1-31-47-61-79-1,457-1,891-2,209-2,449-2,867-3,713-4,819-68,479-88,877-115,103-134,749-149,389-174,511-226,493-4,177,219-5,409,841-7,021,283-10,645,171-330,000,301

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