Q: What are the factor combinations of the number 30,771,629?

 A:
Positive:   1 x 307716297 x 4395947149 x 206521163 x 188783181 x 1700091043 x 295031141 x 269691267 x 24287
Negative: -1 x -30771629-7 x -4395947-149 x -206521-163 x -188783-181 x -170009-1043 x -29503-1141 x -26969-1267 x -24287


How do I find the factor combinations of the number 30,771,629?

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 30,771,629, 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 30,771,629
-1 -30,771,629

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 30,771,629.

Example:
1 x 30,771,629 = 30,771,629
and
-1 x -30,771,629 = 30,771,629
Notice both answers equal 30,771,629

With that explanation out of the way, let's continue. Next, we take the number 30,771,629 and divide it by 2:

30,771,629 ÷ 2 = 15,385,814.5

If the quotient is a whole number, then 2 and 15,385,814.5 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 30,771,629
-1 -30,771,629

Now, we try dividing 30,771,629 by 3:

30,771,629 ÷ 3 = 10,257,209.6667

If the quotient is a whole number, then 3 and 10,257,209.6667 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 30,771,629
-1 -30,771,629

Let's try dividing by 4:

30,771,629 ÷ 4 = 7,692,907.25

If the quotient is a whole number, then 4 and 7,692,907.25 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 30,771,629
-1 30,771,629
Keep dividing by the next highest number until you cannot divide anymore.

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

171491631811,0431,1411,26724,28726,96929,503170,009188,783206,5214,395,94730,771,629
-1-7-149-163-181-1,043-1,141-1,267-24,287-26,969-29,503-170,009-188,783-206,521-4,395,947-30,771,629

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