Q: What are the factor combinations of the number 502,351?

 A:
Positive:   1 x 502351227 x 2213
Negative: -1 x -502351-227 x -2213


How do I find the factor combinations of the number 502,351?

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 502,351, 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.

1 502,351
-1 -502,351

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 502,351.

Example:
1 x 502,351 = 502,351
and
-1 x -502,351 = 502,351
Notice both answers equal 502,351

With that explanation out of the way, let's continue. Next, we take the number 502,351 and divide it by 2:

502,351 ÷ 2 = 251,175.5

If the quotient is a whole number, then 2 and 251,175.5 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:

1 502,351
-1 -502,351

Now, we try dividing 502,351 by 3:

502,351 ÷ 3 = 167,450.3333

If the quotient is a whole number, then 3 and 167,450.3333 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:

1 502,351
-1 -502,351

Let's try dividing by 4:

502,351 ÷ 4 = 125,587.75

If the quotient is a whole number, then 4 and 125,587.75 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:

1 502,351
-1 502,351
Keep dividing by the next highest number until you cannot divide anymore.

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

12272,213502,351
-1-227-2,213-502,351

More Examples

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