Q: What are the factor combinations of the number 30,420,767?

 A:
Positive:   1 x 3042076713 x 234005919 x 160109379 x 385073247 x 1231611027 x 296211501 x 202671559 x 19513
Negative: -1 x -30420767-13 x -2340059-19 x -1601093-79 x -385073-247 x -123161-1027 x -29621-1501 x -20267-1559 x -19513


How do I find the factor combinations of the number 30,420,767?

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 30,420,767, 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 30,420,767
-1 -30,420,767

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 30,420,767.

Example:
1 x 30,420,767 = 30,420,767
and
-1 x -30,420,767 = 30,420,767
Notice both answers equal 30,420,767

With that explanation out of the way, let's continue. Next, we take the number 30,420,767 and divide it by 2:

30,420,767 ÷ 2 = 15,210,383.5

If the quotient is a whole number, then 2 and 15,210,383.5 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 30,420,767
-1 -30,420,767

Now, we try dividing 30,420,767 by 3:

30,420,767 ÷ 3 = 10,140,255.6667

If the quotient is a whole number, then 3 and 10,140,255.6667 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 30,420,767
-1 -30,420,767

Let's try dividing by 4:

30,420,767 ÷ 4 = 7,605,191.75

If the quotient is a whole number, then 4 and 7,605,191.75 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 30,420,767
-1 30,420,767
Keep dividing by the next highest number until you cannot divide anymore.

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

11319792471,0271,5011,55919,51320,26729,621123,161385,0731,601,0932,340,05930,420,767
-1-13-19-79-247-1,027-1,501-1,559-19,513-20,267-29,621-123,161-385,073-1,601,093-2,340,059-30,420,767

More Examples

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