Q: What are the factor combinations of the number 521,525,075?

 A:
Positive:   1 x 5215250755 x 10430501525 x 20861003613 x 8507753065 x 17015515325 x 34031
Negative: -1 x -521525075-5 x -104305015-25 x -20861003-613 x -850775-3065 x -170155-15325 x -34031


How do I find the factor combinations of the number 521,525,075?

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 521,525,075, 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.

1 521,525,075
-1 -521,525,075

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 521,525,075.

Example:
1 x 521,525,075 = 521,525,075
and
-1 x -521,525,075 = 521,525,075
Notice both answers equal 521,525,075

With that explanation out of the way, let's continue. Next, we take the number 521,525,075 and divide it by 2:

521,525,075 ÷ 2 = 260,762,537.5

If the quotient is a whole number, then 2 and 260,762,537.5 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:

1 521,525,075
-1 -521,525,075

Now, we try dividing 521,525,075 by 3:

521,525,075 ÷ 3 = 173,841,691.6667

If the quotient is a whole number, then 3 and 173,841,691.6667 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:

1 521,525,075
-1 -521,525,075

Let's try dividing by 4:

521,525,075 ÷ 4 = 130,381,268.75

If the quotient is a whole number, then 4 and 130,381,268.75 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:

1 521,525,075
-1 521,525,075
Keep dividing by the next highest number until you cannot divide anymore.

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

15256133,06515,32534,031170,155850,77520,861,003104,305,015521,525,075
-1-5-25-613-3,065-15,325-34,031-170,155-850,775-20,861,003-104,305,015-521,525,075

More Examples

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