Q: What are the factor combinations of the number 510,500,065?

 A:
Positive:   1 x 5105000655 x 10210001323 x 22195655115 x 4439131491 x 10397152455 x 2079439041 x 5646511293 x 45205
Negative: -1 x -510500065-5 x -102100013-23 x -22195655-115 x -4439131-491 x -1039715-2455 x -207943-9041 x -56465-11293 x -45205


How do I find the factor combinations of the number 510,500,065?

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 510,500,065, 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.

1 510,500,065
-1 -510,500,065

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 510,500,065.

Example:
1 x 510,500,065 = 510,500,065
and
-1 x -510,500,065 = 510,500,065
Notice both answers equal 510,500,065

With that explanation out of the way, let's continue. Next, we take the number 510,500,065 and divide it by 2:

510,500,065 ÷ 2 = 255,250,032.5

If the quotient is a whole number, then 2 and 255,250,032.5 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:

1 510,500,065
-1 -510,500,065

Now, we try dividing 510,500,065 by 3:

510,500,065 ÷ 3 = 170,166,688.3333

If the quotient is a whole number, then 3 and 170,166,688.3333 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:

1 510,500,065
-1 -510,500,065

Let's try dividing by 4:

510,500,065 ÷ 4 = 127,625,016.25

If the quotient is a whole number, then 4 and 127,625,016.25 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:

1 510,500,065
-1 510,500,065
Keep dividing by the next highest number until you cannot divide anymore.

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

15231154912,4559,04111,29345,20556,465207,9431,039,7154,439,13122,195,655102,100,013510,500,065
-1-5-23-115-491-2,455-9,041-11,293-45,205-56,465-207,943-1,039,715-4,439,131-22,195,655-102,100,013-510,500,065

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