Q: What are the factor combinations of the number 507,395?

 A:
Positive:   1 x 5073955 x 1014797 x 7248519 x 2670535 x 1449749 x 1035595 x 5341109 x 4655133 x 3815245 x 2071545 x 931665 x 763
Negative: -1 x -507395-5 x -101479-7 x -72485-19 x -26705-35 x -14497-49 x -10355-95 x -5341-109 x -4655-133 x -3815-245 x -2071-545 x -931-665 x -763


How do I find the factor combinations of the number 507,395?

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 507,395, 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.

1 507,395
-1 -507,395

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 507,395.

Example:
1 x 507,395 = 507,395
and
-1 x -507,395 = 507,395
Notice both answers equal 507,395

With that explanation out of the way, let's continue. Next, we take the number 507,395 and divide it by 2:

507,395 ÷ 2 = 253,697.5

If the quotient is a whole number, then 2 and 253,697.5 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:

1 507,395
-1 -507,395

Now, we try dividing 507,395 by 3:

507,395 ÷ 3 = 169,131.6667

If the quotient is a whole number, then 3 and 169,131.6667 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:

1 507,395
-1 -507,395

Let's try dividing by 4:

507,395 ÷ 4 = 126,848.75

If the quotient is a whole number, then 4 and 126,848.75 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:

1 507,395
-1 507,395
Keep dividing by the next highest number until you cannot divide anymore.

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

157193549951091332455456657639312,0713,8154,6555,34110,35514,49726,70572,485101,479507,395
-1-5-7-19-35-49-95-109-133-245-545-665-763-931-2,071-3,815-4,655-5,341-10,355-14,497-26,705-72,485-101,479-507,395

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