Q: What are the factor combinations of the number 33,144,133?

 A:
Positive:   1 x 3314413311 x 301310353 x 625361139 x 238447409 x 81037583 x 568511529 x 216774499 x 7367
Negative: -1 x -33144133-11 x -3013103-53 x -625361-139 x -238447-409 x -81037-583 x -56851-1529 x -21677-4499 x -7367


How do I find the factor combinations of the number 33,144,133?

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 33,144,133, 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 33,144,133
-1 -33,144,133

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 33,144,133.

Example:
1 x 33,144,133 = 33,144,133
and
-1 x -33,144,133 = 33,144,133
Notice both answers equal 33,144,133

With that explanation out of the way, let's continue. Next, we take the number 33,144,133 and divide it by 2:

33,144,133 ÷ 2 = 16,572,066.5

If the quotient is a whole number, then 2 and 16,572,066.5 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 33,144,133
-1 -33,144,133

Now, we try dividing 33,144,133 by 3:

33,144,133 ÷ 3 = 11,048,044.3333

If the quotient is a whole number, then 3 and 11,048,044.3333 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 33,144,133
-1 -33,144,133

Let's try dividing by 4:

33,144,133 ÷ 4 = 8,286,033.25

If the quotient is a whole number, then 4 and 8,286,033.25 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 33,144,133
-1 33,144,133
Keep dividing by the next highest number until you cannot divide anymore.

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

111531394095831,5294,4997,36721,67756,85181,037238,447625,3613,013,10333,144,133
-1-11-53-139-409-583-1,529-4,499-7,367-21,677-56,851-81,037-238,447-625,361-3,013,103-33,144,133

More Examples

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