Q: What are the factor combinations of the number 212,023,123?

 A:
Positive:   1 x 21202312313 x 1630947179 x 2683837431 x 491933479 x 4426371027 x 2064495603 x 378416227 x 34049
Negative: -1 x -212023123-13 x -16309471-79 x -2683837-431 x -491933-479 x -442637-1027 x -206449-5603 x -37841-6227 x -34049


How do I find the factor combinations of the number 212,023,123?

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 212,023,123, 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.

1 212,023,123
-1 -212,023,123

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 212,023,123.

Example:
1 x 212,023,123 = 212,023,123
and
-1 x -212,023,123 = 212,023,123
Notice both answers equal 212,023,123

With that explanation out of the way, let's continue. Next, we take the number 212,023,123 and divide it by 2:

212,023,123 ÷ 2 = 106,011,561.5

If the quotient is a whole number, then 2 and 106,011,561.5 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:

1 212,023,123
-1 -212,023,123

Now, we try dividing 212,023,123 by 3:

212,023,123 ÷ 3 = 70,674,374.3333

If the quotient is a whole number, then 3 and 70,674,374.3333 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:

1 212,023,123
-1 -212,023,123

Let's try dividing by 4:

212,023,123 ÷ 4 = 53,005,780.75

If the quotient is a whole number, then 4 and 53,005,780.75 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:

1 212,023,123
-1 212,023,123
Keep dividing by the next highest number until you cannot divide anymore.

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

113794314791,0275,6036,22734,04937,841206,449442,637491,9332,683,83716,309,471212,023,123
-1-13-79-431-479-1,027-5,603-6,227-34,049-37,841-206,449-442,637-491,933-2,683,837-16,309,471-212,023,123

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