Q: What are the factor combinations of the number 103,110,311?

 A:
Positive:   1 x 10311031123 x 4483057
Negative: -1 x -103110311-23 x -4483057


How do I find the factor combinations of the number 103,110,311?

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 103,110,311, 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.

1 103,110,311
-1 -103,110,311

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 103,110,311.

Example:
1 x 103,110,311 = 103,110,311
and
-1 x -103,110,311 = 103,110,311
Notice both answers equal 103,110,311

With that explanation out of the way, let's continue. Next, we take the number 103,110,311 and divide it by 2:

103,110,311 ÷ 2 = 51,555,155.5

If the quotient is a whole number, then 2 and 51,555,155.5 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:

1 103,110,311
-1 -103,110,311

Now, we try dividing 103,110,311 by 3:

103,110,311 ÷ 3 = 34,370,103.6667

If the quotient is a whole number, then 3 and 34,370,103.6667 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:

1 103,110,311
-1 -103,110,311

Let's try dividing by 4:

103,110,311 ÷ 4 = 25,777,577.75

If the quotient is a whole number, then 4 and 25,777,577.75 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:

1 103,110,311
-1 103,110,311
Keep dividing by the next highest number until you cannot divide anymore.

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

1234,483,057103,110,311
-1-23-4,483,057-103,110,311

More Examples

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