Q: What are the factor combinations of the number 512,375?

 A:
Positive:   1 x 5123755 x 10247525 x 20495125 x 4099
Negative: -1 x -512375-5 x -102475-25 x -20495-125 x -4099


How do I find the factor combinations of the number 512,375?

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 512,375, 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.

1 512,375
-1 -512,375

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 512,375.

Example:
1 x 512,375 = 512,375
and
-1 x -512,375 = 512,375
Notice both answers equal 512,375

With that explanation out of the way, let's continue. Next, we take the number 512,375 and divide it by 2:

512,375 ÷ 2 = 256,187.5

If the quotient is a whole number, then 2 and 256,187.5 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:

1 512,375
-1 -512,375

Now, we try dividing 512,375 by 3:

512,375 ÷ 3 = 170,791.6667

If the quotient is a whole number, then 3 and 170,791.6667 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:

1 512,375
-1 -512,375

Let's try dividing by 4:

512,375 ÷ 4 = 128,093.75

If the quotient is a whole number, then 4 and 128,093.75 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:

1 512,375
-1 512,375
Keep dividing by the next highest number until you cannot divide anymore.

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

15251254,09920,495102,475512,375
-1-5-25-125-4,099-20,495-102,475-512,375

More Examples

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