Q: What are the factor combinations of the number 508,812?

 A:
Positive:   1 x 5088122 x 2544063 x 1696044 x 1272036 x 8480212 x 42401109 x 4668218 x 2334327 x 1556389 x 1308436 x 1167654 x 778
Negative: -1 x -508812-2 x -254406-3 x -169604-4 x -127203-6 x -84802-12 x -42401-109 x -4668-218 x -2334-327 x -1556-389 x -1308-436 x -1167-654 x -778


How do I find the factor combinations of the number 508,812?

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 508,812, 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.

1 508,812
-1 -508,812

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 508,812.

Example:
1 x 508,812 = 508,812
and
-1 x -508,812 = 508,812
Notice both answers equal 508,812

With that explanation out of the way, let's continue. Next, we take the number 508,812 and divide it by 2:

508,812 ÷ 2 = 254,406

If the quotient is a whole number, then 2 and 254,406 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 2 254,406 508,812
-1 -2 -254,406 -508,812

Now, we try dividing 508,812 by 3:

508,812 ÷ 3 = 169,604

If the quotient is a whole number, then 3 and 169,604 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 3 169,604 254,406 508,812
-1 -2 -3 -169,604 -254,406 -508,812

Let's try dividing by 4:

508,812 ÷ 4 = 127,203

If the quotient is a whole number, then 4 and 127,203 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 4 127,203 169,604 254,406 508,812
-1 -2 -3 -4 -127,203 -169,604 -254,406 508,812
Keep dividing by the next highest number until you cannot divide anymore.

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

12346121092183273894366547781,1671,3081,5562,3344,66842,40184,802127,203169,604254,406508,812
-1-2-3-4-6-12-109-218-327-389-436-654-778-1,167-1,308-1,556-2,334-4,668-42,401-84,802-127,203-169,604-254,406-508,812

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