Q: What are the factor combinations of the number 52,123,121?

 A:
Positive:   1 x 5212312129 x 179734931 x 168139137 x 1408733899 x 579791073 x 485771147 x 454431567 x 33263
Negative: -1 x -52123121-29 x -1797349-31 x -1681391-37 x -1408733-899 x -57979-1073 x -48577-1147 x -45443-1567 x -33263


How do I find the factor combinations of the number 52,123,121?

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 52,123,121, 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 52,123,121
-1 -52,123,121

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 52,123,121.

Example:
1 x 52,123,121 = 52,123,121
and
-1 x -52,123,121 = 52,123,121
Notice both answers equal 52,123,121

With that explanation out of the way, let's continue. Next, we take the number 52,123,121 and divide it by 2:

52,123,121 ÷ 2 = 26,061,560.5

If the quotient is a whole number, then 2 and 26,061,560.5 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 52,123,121
-1 -52,123,121

Now, we try dividing 52,123,121 by 3:

52,123,121 ÷ 3 = 17,374,373.6667

If the quotient is a whole number, then 3 and 17,374,373.6667 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 52,123,121
-1 -52,123,121

Let's try dividing by 4:

52,123,121 ÷ 4 = 13,030,780.25

If the quotient is a whole number, then 4 and 13,030,780.25 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 52,123,121
-1 52,123,121
Keep dividing by the next highest number until you cannot divide anymore.

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

12931378991,0731,1471,56733,26345,44348,57757,9791,408,7331,681,3911,797,34952,123,121
-1-29-31-37-899-1,073-1,147-1,567-33,263-45,443-48,577-57,979-1,408,733-1,681,391-1,797,349-52,123,121

More Examples

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