Q: What are the factor combinations of the number 30,421,013?

 A:
Positive:   1 x 304210137 x 434585931 x 98132349 x 620837217 x 140189343 x 886911519 x 200272861 x 10633
Negative: -1 x -30421013-7 x -4345859-31 x -981323-49 x -620837-217 x -140189-343 x -88691-1519 x -20027-2861 x -10633


How do I find the factor combinations of the number 30,421,013?

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 30,421,013, 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 30,421,013
-1 -30,421,013

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 30,421,013.

Example:
1 x 30,421,013 = 30,421,013
and
-1 x -30,421,013 = 30,421,013
Notice both answers equal 30,421,013

With that explanation out of the way, let's continue. Next, we take the number 30,421,013 and divide it by 2:

30,421,013 ÷ 2 = 15,210,506.5

If the quotient is a whole number, then 2 and 15,210,506.5 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 30,421,013
-1 -30,421,013

Now, we try dividing 30,421,013 by 3:

30,421,013 ÷ 3 = 10,140,337.6667

If the quotient is a whole number, then 3 and 10,140,337.6667 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 30,421,013
-1 -30,421,013

Let's try dividing by 4:

30,421,013 ÷ 4 = 7,605,253.25

If the quotient is a whole number, then 4 and 7,605,253.25 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 30,421,013
-1 30,421,013
Keep dividing by the next highest number until you cannot divide anymore.

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

1731492173431,5192,86110,63320,02788,691140,189620,837981,3234,345,85930,421,013
-1-7-31-49-217-343-1,519-2,861-10,633-20,027-88,691-140,189-620,837-981,323-4,345,859-30,421,013

More Examples

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