Q: What are the factor combinations of the number 510,575,075?

 A:
Positive:   1 x 5105750755 x 10211501525 x 20423003109 x 4684175545 x 9368352725 x 187367
Negative: -1 x -510575075-5 x -102115015-25 x -20423003-109 x -4684175-545 x -936835-2725 x -187367


How do I find the factor combinations of the number 510,575,075?

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 510,575,075, 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.

1 510,575,075
-1 -510,575,075

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 510,575,075.

Example:
1 x 510,575,075 = 510,575,075
and
-1 x -510,575,075 = 510,575,075
Notice both answers equal 510,575,075

With that explanation out of the way, let's continue. Next, we take the number 510,575,075 and divide it by 2:

510,575,075 ÷ 2 = 255,287,537.5

If the quotient is a whole number, then 2 and 255,287,537.5 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:

1 510,575,075
-1 -510,575,075

Now, we try dividing 510,575,075 by 3:

510,575,075 ÷ 3 = 170,191,691.6667

If the quotient is a whole number, then 3 and 170,191,691.6667 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:

1 510,575,075
-1 -510,575,075

Let's try dividing by 4:

510,575,075 ÷ 4 = 127,643,768.75

If the quotient is a whole number, then 4 and 127,643,768.75 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:

1 510,575,075
-1 510,575,075
Keep dividing by the next highest number until you cannot divide anymore.

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

15251095452,725187,367936,8354,684,17520,423,003102,115,015510,575,075
-1-5-25-109-545-2,725-187,367-936,835-4,684,175-20,423,003-102,115,015-510,575,075

More Examples

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