Q: What are the factor combinations of the number 508,676?

 A:
Positive:   1 x 5086762 x 2543384 x 1271697 x 7266814 x 3633428 x 1816737 x 1374874 x 6874148 x 3437259 x 1964491 x 1036518 x 982
Negative: -1 x -508676-2 x -254338-4 x -127169-7 x -72668-14 x -36334-28 x -18167-37 x -13748-74 x -6874-148 x -3437-259 x -1964-491 x -1036-518 x -982


How do I find the factor combinations of the number 508,676?

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 508,676, 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.

1 508,676
-1 -508,676

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 508,676.

Example:
1 x 508,676 = 508,676
and
-1 x -508,676 = 508,676
Notice both answers equal 508,676

With that explanation out of the way, let's continue. Next, we take the number 508,676 and divide it by 2:

508,676 ÷ 2 = 254,338

If the quotient is a whole number, then 2 and 254,338 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 2 254,338 508,676
-1 -2 -254,338 -508,676

Now, we try dividing 508,676 by 3:

508,676 ÷ 3 = 169,558.6667

If the quotient is a whole number, then 3 and 169,558.6667 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 2 254,338 508,676
-1 -2 -254,338 -508,676

Let's try dividing by 4:

508,676 ÷ 4 = 127,169

If the quotient is a whole number, then 4 and 127,169 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 4 127,169 254,338 508,676
-1 -2 -4 -127,169 -254,338 508,676
Keep dividing by the next highest number until you cannot divide anymore.

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

1247142837741482594915189821,0361,9643,4376,87413,74818,16736,33472,668127,169254,338508,676
-1-2-4-7-14-28-37-74-148-259-491-518-982-1,036-1,964-3,437-6,874-13,748-18,167-36,334-72,668-127,169-254,338-508,676

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