Q: What are the factor combinations of the number 505,240,519?

 A:
Positive:   1 x 5052405197 x 7217721749 x 1031103173 x 6921103137 x 3687887511 x 988729959 x 5268411031 x 4900493577 x 1412476713 x 752637217 x 7000710001 x 50519
Negative: -1 x -505240519-7 x -72177217-49 x -10311031-73 x -6921103-137 x -3687887-511 x -988729-959 x -526841-1031 x -490049-3577 x -141247-6713 x -75263-7217 x -70007-10001 x -50519


How do I find the factor combinations of the number 505,240,519?

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 505,240,519, 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.

1 505,240,519
-1 -505,240,519

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 505,240,519.

Example:
1 x 505,240,519 = 505,240,519
and
-1 x -505,240,519 = 505,240,519
Notice both answers equal 505,240,519

With that explanation out of the way, let's continue. Next, we take the number 505,240,519 and divide it by 2:

505,240,519 ÷ 2 = 252,620,259.5

If the quotient is a whole number, then 2 and 252,620,259.5 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:

1 505,240,519
-1 -505,240,519

Now, we try dividing 505,240,519 by 3:

505,240,519 ÷ 3 = 168,413,506.3333

If the quotient is a whole number, then 3 and 168,413,506.3333 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:

1 505,240,519
-1 -505,240,519

Let's try dividing by 4:

505,240,519 ÷ 4 = 126,310,129.75

If the quotient is a whole number, then 4 and 126,310,129.75 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:

1 505,240,519
-1 505,240,519
Keep dividing by the next highest number until you cannot divide anymore.

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

1749731375119591,0313,5776,7137,21710,00150,51970,00775,263141,247490,049526,841988,7293,687,8876,921,10310,311,03172,177,217505,240,519
-1-7-49-73-137-511-959-1,031-3,577-6,713-7,217-10,001-50,519-70,007-75,263-141,247-490,049-526,841-988,729-3,687,887-6,921,103-10,311,031-72,177,217-505,240,519

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