Q: What are the factor combinations of the number 133,311,233?

 A:
Positive:   1 x 13331123311 x 1211920371 x 1877623131 x 1017643781 x 1706931303 x 1023111441 x 925139301 x 14333
Negative: -1 x -133311233-11 x -12119203-71 x -1877623-131 x -1017643-781 x -170693-1303 x -102311-1441 x -92513-9301 x -14333


How do I find the factor combinations of the number 133,311,233?

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 133,311,233, 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.

1 133,311,233
-1 -133,311,233

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 133,311,233.

Example:
1 x 133,311,233 = 133,311,233
and
-1 x -133,311,233 = 133,311,233
Notice both answers equal 133,311,233

With that explanation out of the way, let's continue. Next, we take the number 133,311,233 and divide it by 2:

133,311,233 ÷ 2 = 66,655,616.5

If the quotient is a whole number, then 2 and 66,655,616.5 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:

1 133,311,233
-1 -133,311,233

Now, we try dividing 133,311,233 by 3:

133,311,233 ÷ 3 = 44,437,077.6667

If the quotient is a whole number, then 3 and 44,437,077.6667 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:

1 133,311,233
-1 -133,311,233

Let's try dividing by 4:

133,311,233 ÷ 4 = 33,327,808.25

If the quotient is a whole number, then 4 and 33,327,808.25 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:

1 133,311,233
-1 133,311,233
Keep dividing by the next highest number until you cannot divide anymore.

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

111711317811,3031,4419,30114,33392,513102,311170,6931,017,6431,877,62312,119,203133,311,233
-1-11-71-131-781-1,303-1,441-9,301-14,333-92,513-102,311-170,693-1,017,643-1,877,623-12,119,203-133,311,233

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