Q: What are the factor combinations of the number 335,225,223?

 A:
Positive:   1 x 3352252233 x 1117417419 x 3724724727 x 1241574981 x 4138583
Negative: -1 x -335225223-3 x -111741741-9 x -37247247-27 x -12415749-81 x -4138583


How do I find the factor combinations of the number 335,225,223?

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 335,225,223, 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.

1 335,225,223
-1 -335,225,223

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 335,225,223.

Example:
1 x 335,225,223 = 335,225,223
and
-1 x -335,225,223 = 335,225,223
Notice both answers equal 335,225,223

With that explanation out of the way, let's continue. Next, we take the number 335,225,223 and divide it by 2:

335,225,223 ÷ 2 = 167,612,611.5

If the quotient is a whole number, then 2 and 167,612,611.5 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:

1 335,225,223
-1 -335,225,223

Now, we try dividing 335,225,223 by 3:

335,225,223 ÷ 3 = 111,741,741

If the quotient is a whole number, then 3 and 111,741,741 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 111,741,741 335,225,223
-1 -3 -111,741,741 -335,225,223

Let's try dividing by 4:

335,225,223 ÷ 4 = 83,806,305.75

If the quotient is a whole number, then 4 and 83,806,305.75 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 3 111,741,741 335,225,223
-1 -3 -111,741,741 335,225,223
Keep dividing by the next highest number until you cannot divide anymore.

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

13927814,138,58312,415,74937,247,247111,741,741335,225,223
-1-3-9-27-81-4,138,583-12,415,749-37,247,247-111,741,741-335,225,223

More Examples

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