Q: What are the factor combinations of the number 510,308,821?

 A:
Positive:   1 x 51030882111 x 4639171119 x 2685835943 x 11867647209 x 2441669473 x 1078877817 x 6246138987 x 56783
Negative: -1 x -510308821-11 x -46391711-19 x -26858359-43 x -11867647-209 x -2441669-473 x -1078877-817 x -624613-8987 x -56783


How do I find the factor combinations of the number 510,308,821?

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 510,308,821, 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.

1 510,308,821
-1 -510,308,821

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 510,308,821.

Example:
1 x 510,308,821 = 510,308,821
and
-1 x -510,308,821 = 510,308,821
Notice both answers equal 510,308,821

With that explanation out of the way, let's continue. Next, we take the number 510,308,821 and divide it by 2:

510,308,821 ÷ 2 = 255,154,410.5

If the quotient is a whole number, then 2 and 255,154,410.5 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:

1 510,308,821
-1 -510,308,821

Now, we try dividing 510,308,821 by 3:

510,308,821 ÷ 3 = 170,102,940.3333

If the quotient is a whole number, then 3 and 170,102,940.3333 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:

1 510,308,821
-1 -510,308,821

Let's try dividing by 4:

510,308,821 ÷ 4 = 127,577,205.25

If the quotient is a whole number, then 4 and 127,577,205.25 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:

1 510,308,821
-1 510,308,821
Keep dividing by the next highest number until you cannot divide anymore.

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

11119432094738178,98756,783624,6131,078,8772,441,66911,867,64726,858,35946,391,711510,308,821
-1-11-19-43-209-473-817-8,987-56,783-624,613-1,078,877-2,441,669-11,867,647-26,858,359-46,391,711-510,308,821

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