Q: What are the factor combinations of the number 412,054,027?

 A:
Positive:   1 x 4120540277 x 5886486111 x 3745945777 x 5351351
Negative: -1 x -412054027-7 x -58864861-11 x -37459457-77 x -5351351


How do I find the factor combinations of the number 412,054,027?

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 412,054,027, 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.

1 412,054,027
-1 -412,054,027

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 412,054,027.

Example:
1 x 412,054,027 = 412,054,027
and
-1 x -412,054,027 = 412,054,027
Notice both answers equal 412,054,027

With that explanation out of the way, let's continue. Next, we take the number 412,054,027 and divide it by 2:

412,054,027 ÷ 2 = 206,027,013.5

If the quotient is a whole number, then 2 and 206,027,013.5 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:

1 412,054,027
-1 -412,054,027

Now, we try dividing 412,054,027 by 3:

412,054,027 ÷ 3 = 137,351,342.3333

If the quotient is a whole number, then 3 and 137,351,342.3333 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:

1 412,054,027
-1 -412,054,027

Let's try dividing by 4:

412,054,027 ÷ 4 = 103,013,506.75

If the quotient is a whole number, then 4 and 103,013,506.75 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:

1 412,054,027
-1 412,054,027
Keep dividing by the next highest number until you cannot divide anymore.

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

1711775,351,35137,459,45758,864,861412,054,027
-1-7-11-77-5,351,351-37,459,457-58,864,861-412,054,027

More Examples

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