Q: What are the factor combinations of the number 103,103,329?

 A:
Positive:   1 x 1031033297 x 1472904719 x 5426491133 x 775213173 x 5959731211 x 851393287 x 313674481 x 23009
Negative: -1 x -103103329-7 x -14729047-19 x -5426491-133 x -775213-173 x -595973-1211 x -85139-3287 x -31367-4481 x -23009


How do I find the factor combinations of the number 103,103,329?

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 103,103,329, 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.

1 103,103,329
-1 -103,103,329

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 103,103,329.

Example:
1 x 103,103,329 = 103,103,329
and
-1 x -103,103,329 = 103,103,329
Notice both answers equal 103,103,329

With that explanation out of the way, let's continue. Next, we take the number 103,103,329 and divide it by 2:

103,103,329 ÷ 2 = 51,551,664.5

If the quotient is a whole number, then 2 and 51,551,664.5 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:

1 103,103,329
-1 -103,103,329

Now, we try dividing 103,103,329 by 3:

103,103,329 ÷ 3 = 34,367,776.3333

If the quotient is a whole number, then 3 and 34,367,776.3333 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:

1 103,103,329
-1 -103,103,329

Let's try dividing by 4:

103,103,329 ÷ 4 = 25,775,832.25

If the quotient is a whole number, then 4 and 25,775,832.25 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:

1 103,103,329
-1 103,103,329
Keep dividing by the next highest number until you cannot divide anymore.

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

17191331731,2113,2874,48123,00931,36785,139595,973775,2135,426,49114,729,047103,103,329
-1-7-19-133-173-1,211-3,287-4,481-23,009-31,367-85,139-595,973-775,213-5,426,491-14,729,047-103,103,329

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