Q: What are the factor combinations of the number 330,442,021?

 A:
Positive:   1 x 3304420217 x 4720600313 x 2541861791 x 3631231269 x 12284091883 x 1754873497 x 9449313499 x 24479
Negative: -1 x -330442021-7 x -47206003-13 x -25418617-91 x -3631231-269 x -1228409-1883 x -175487-3497 x -94493-13499 x -24479


How do I find the factor combinations of the number 330,442,021?

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 330,442,021, 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.

1 330,442,021
-1 -330,442,021

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 330,442,021.

Example:
1 x 330,442,021 = 330,442,021
and
-1 x -330,442,021 = 330,442,021
Notice both answers equal 330,442,021

With that explanation out of the way, let's continue. Next, we take the number 330,442,021 and divide it by 2:

330,442,021 ÷ 2 = 165,221,010.5

If the quotient is a whole number, then 2 and 165,221,010.5 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:

1 330,442,021
-1 -330,442,021

Now, we try dividing 330,442,021 by 3:

330,442,021 ÷ 3 = 110,147,340.3333

If the quotient is a whole number, then 3 and 110,147,340.3333 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:

1 330,442,021
-1 -330,442,021

Let's try dividing by 4:

330,442,021 ÷ 4 = 82,610,505.25

If the quotient is a whole number, then 4 and 82,610,505.25 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:

1 330,442,021
-1 330,442,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1713912691,8833,49713,49924,47994,493175,4871,228,4093,631,23125,418,61747,206,003330,442,021
-1-7-13-91-269-1,883-3,497-13,499-24,479-94,493-175,487-1,228,409-3,631,231-25,418,617-47,206,003-330,442,021

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