Q: What are the factor combinations of the number 33,638,225?

 A:
Positive:   1 x 336382255 x 672764525 x 1345529827 x 406751627 x 206754135 x 8135
Negative: -1 x -33638225-5 x -6727645-25 x -1345529-827 x -40675-1627 x -20675-4135 x -8135


How do I find the factor combinations of the number 33,638,225?

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 33,638,225, 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 33,638,225
-1 -33,638,225

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 33,638,225.

Example:
1 x 33,638,225 = 33,638,225
and
-1 x -33,638,225 = 33,638,225
Notice both answers equal 33,638,225

With that explanation out of the way, let's continue. Next, we take the number 33,638,225 and divide it by 2:

33,638,225 ÷ 2 = 16,819,112.5

If the quotient is a whole number, then 2 and 16,819,112.5 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 33,638,225
-1 -33,638,225

Now, we try dividing 33,638,225 by 3:

33,638,225 ÷ 3 = 11,212,741.6667

If the quotient is a whole number, then 3 and 11,212,741.6667 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 33,638,225
-1 -33,638,225

Let's try dividing by 4:

33,638,225 ÷ 4 = 8,409,556.25

If the quotient is a whole number, then 4 and 8,409,556.25 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 33,638,225
-1 33,638,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15258271,6274,1358,13520,67540,6751,345,5296,727,64533,638,225
-1-5-25-827-1,627-4,135-8,135-20,675-40,675-1,345,529-6,727,645-33,638,225

More Examples

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