Q: What are the factor combinations of the number 501,678?

 A:
Positive:   1 x 5016782 x 2508393 x 1672266 x 836139 x 5574218 x 2787147 x 1067494 x 5337141 x 3558282 x 1779423 x 1186593 x 846
Negative: -1 x -501678-2 x -250839-3 x -167226-6 x -83613-9 x -55742-18 x -27871-47 x -10674-94 x -5337-141 x -3558-282 x -1779-423 x -1186-593 x -846


How do I find the factor combinations of the number 501,678?

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 501,678, 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.

1 501,678
-1 -501,678

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 501,678.

Example:
1 x 501,678 = 501,678
and
-1 x -501,678 = 501,678
Notice both answers equal 501,678

With that explanation out of the way, let's continue. Next, we take the number 501,678 and divide it by 2:

501,678 ÷ 2 = 250,839

If the quotient is a whole number, then 2 and 250,839 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 2 250,839 501,678
-1 -2 -250,839 -501,678

Now, we try dividing 501,678 by 3:

501,678 ÷ 3 = 167,226

If the quotient is a whole number, then 3 and 167,226 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 2 3 167,226 250,839 501,678
-1 -2 -3 -167,226 -250,839 -501,678

Let's try dividing by 4:

501,678 ÷ 4 = 125,419.5

If the quotient is a whole number, then 4 and 125,419.5 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 2 3 167,226 250,839 501,678
-1 -2 -3 -167,226 -250,839 501,678
Keep dividing by the next highest number until you cannot divide anymore.

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

123691847941412824235938461,1861,7793,5585,33710,67427,87155,74283,613167,226250,839501,678
-1-2-3-6-9-18-47-94-141-282-423-593-846-1,186-1,779-3,558-5,337-10,674-27,871-55,742-83,613-167,226-250,839-501,678

More Examples

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