# Q: What are the factor combinations of the number 515,432?

A:
Positive:   1 x 5154322 x 2577164 x 1288588 x 6442919 x 2712838 x 1356476 x 6782152 x 3391
Negative: -1 x -515432-2 x -257716-4 x -128858-8 x -64429-19 x -27128-38 x -13564-76 x -6782-152 x -3391

## How do I find the factor combinations of the number 515,432?

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 515,432, 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.

 1 515,432 -1 -515,432

#### 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 515,432.

Example:
1 x 515,432 = 515,432
and
-1 x -515,432 = 515,432
Notice both answers equal 515,432

With that explanation out of the way, let's continue. Next, we take the number 515,432 and divide it by 2:

515,432 ÷ 2 = 257,716

If the quotient is a whole number, then 2 and 257,716 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

 1 2 257,716 515,432 -1 -2 -257,716 -515,432

Now, we try dividing 515,432 by 3:

515,432 ÷ 3 = 171,810.6667

If the quotient is a whole number, then 3 and 171,810.6667 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 2 257,716 515,432 -1 -2 -257,716 -515,432

Let's try dividing by 4:

515,432 ÷ 4 = 128,858

If the quotient is a whole number, then 4 and 128,858 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

 1 2 4 128,858 257,716 515,432 -1 -2 -4 -128,858 -257,716 515,432
Keep dividing by the next highest number until you cannot divide anymore.

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

 1 2 4 8 19 38 76 152 3,391 6,782 13,564 27,128 64,429 128,858 257,716 515,432 -1 -2 -4 -8 -19 -38 -76 -152 -3,391 -6,782 -13,564 -27,128 -64,429 -128,858 -257,716 -515,432

### More Examples

Here are some more numbers to try:

Try the factor calculator

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