Q: What are the factor combinations of the number 331,253?

 A:
Positive:   1 x 33125313 x 2548183 x 3991307 x 1079
Negative: -1 x -331253-13 x -25481-83 x -3991-307 x -1079


How do I find the factor combinations of the number 331,253?

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 331,253, 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.

1 331,253
-1 -331,253

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 331,253.

Example:
1 x 331,253 = 331,253
and
-1 x -331,253 = 331,253
Notice both answers equal 331,253

With that explanation out of the way, let's continue. Next, we take the number 331,253 and divide it by 2:

331,253 ÷ 2 = 165,626.5

If the quotient is a whole number, then 2 and 165,626.5 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:

1 331,253
-1 -331,253

Now, we try dividing 331,253 by 3:

331,253 ÷ 3 = 110,417.6667

If the quotient is a whole number, then 3 and 110,417.6667 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:

1 331,253
-1 -331,253

Let's try dividing by 4:

331,253 ÷ 4 = 82,813.25

If the quotient is a whole number, then 4 and 82,813.25 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:

1 331,253
-1 331,253
Keep dividing by the next highest number until you cannot divide anymore.

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

113833071,0793,99125,481331,253
-1-13-83-307-1,079-3,991-25,481-331,253

More Examples

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