Q: What are the factor combinations of the number 30,110,509?

 A:
Positive:   1 x 3011050911 x 273731913 x 2316193143 x 210563193 x 1560131091 x 275992123 x 141832509 x 12001
Negative: -1 x -30110509-11 x -2737319-13 x -2316193-143 x -210563-193 x -156013-1091 x -27599-2123 x -14183-2509 x -12001


How do I find the factor combinations of the number 30,110,509?

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 30,110,509, 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 30,110,509
-1 -30,110,509

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 30,110,509.

Example:
1 x 30,110,509 = 30,110,509
and
-1 x -30,110,509 = 30,110,509
Notice both answers equal 30,110,509

With that explanation out of the way, let's continue. Next, we take the number 30,110,509 and divide it by 2:

30,110,509 ÷ 2 = 15,055,254.5

If the quotient is a whole number, then 2 and 15,055,254.5 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 30,110,509
-1 -30,110,509

Now, we try dividing 30,110,509 by 3:

30,110,509 ÷ 3 = 10,036,836.3333

If the quotient is a whole number, then 3 and 10,036,836.3333 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 30,110,509
-1 -30,110,509

Let's try dividing by 4:

30,110,509 ÷ 4 = 7,527,627.25

If the quotient is a whole number, then 4 and 7,527,627.25 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 30,110,509
-1 30,110,509
Keep dividing by the next highest number until you cannot divide anymore.

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

111131431931,0912,1232,50912,00114,18327,599156,013210,5632,316,1932,737,31930,110,509
-1-11-13-143-193-1,091-2,123-2,509-12,001-14,183-27,599-156,013-210,563-2,316,193-2,737,319-30,110,509

More Examples

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