Q: What are the factor combinations of the number 33,135,529?

 A:
Positive:   1 x 331355297 x 4733647
Negative: -1 x -33135529-7 x -4733647


How do I find the factor combinations of the number 33,135,529?

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 33,135,529, 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 33,135,529
-1 -33,135,529

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 33,135,529.

Example:
1 x 33,135,529 = 33,135,529
and
-1 x -33,135,529 = 33,135,529
Notice both answers equal 33,135,529

With that explanation out of the way, let's continue. Next, we take the number 33,135,529 and divide it by 2:

33,135,529 ÷ 2 = 16,567,764.5

If the quotient is a whole number, then 2 and 16,567,764.5 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 33,135,529
-1 -33,135,529

Now, we try dividing 33,135,529 by 3:

33,135,529 ÷ 3 = 11,045,176.3333

If the quotient is a whole number, then 3 and 11,045,176.3333 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 33,135,529
-1 -33,135,529

Let's try dividing by 4:

33,135,529 ÷ 4 = 8,283,882.25

If the quotient is a whole number, then 4 and 8,283,882.25 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 33,135,529
-1 33,135,529
Keep dividing by the next highest number until you cannot divide anymore.

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

174,733,64733,135,529
-1-7-4,733,647-33,135,529

More Examples

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