Q: What are the factor combinations of the number 30,133,013?

 A:
Positive:   1 x 3013301323 x 131013173 x 412781131 x 230023137 x 2199491679 x 179473013 x 100013151 x 9563
Negative: -1 x -30133013-23 x -1310131-73 x -412781-131 x -230023-137 x -219949-1679 x -17947-3013 x -10001-3151 x -9563


How do I find the factor combinations of the number 30,133,013?

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 30,133,013, 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 30,133,013
-1 -30,133,013

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 30,133,013.

Example:
1 x 30,133,013 = 30,133,013
and
-1 x -30,133,013 = 30,133,013
Notice both answers equal 30,133,013

With that explanation out of the way, let's continue. Next, we take the number 30,133,013 and divide it by 2:

30,133,013 ÷ 2 = 15,066,506.5

If the quotient is a whole number, then 2 and 15,066,506.5 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 30,133,013
-1 -30,133,013

Now, we try dividing 30,133,013 by 3:

30,133,013 ÷ 3 = 10,044,337.6667

If the quotient is a whole number, then 3 and 10,044,337.6667 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 30,133,013
-1 -30,133,013

Let's try dividing by 4:

30,133,013 ÷ 4 = 7,533,253.25

If the quotient is a whole number, then 4 and 7,533,253.25 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 30,133,013
-1 30,133,013
Keep dividing by the next highest number until you cannot divide anymore.

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

123731311371,6793,0133,1519,56310,00117,947219,949230,023412,7811,310,13130,133,013
-1-23-73-131-137-1,679-3,013-3,151-9,563-10,001-17,947-219,949-230,023-412,781-1,310,131-30,133,013

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