Q: What are the factor combinations of the number 557,728?

 A:
Positive:   1 x 5577282 x 2788644 x 1394328 x 6971616 x 3485829 x 1923232 x 1742958 x 9616116 x 4808232 x 2404464 x 1202601 x 928
Negative: -1 x -557728-2 x -278864-4 x -139432-8 x -69716-16 x -34858-29 x -19232-32 x -17429-58 x -9616-116 x -4808-232 x -2404-464 x -1202-601 x -928


How do I find the factor combinations of the number 557,728?

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 557,728, 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.

1 557,728
-1 -557,728

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 557,728.

Example:
1 x 557,728 = 557,728
and
-1 x -557,728 = 557,728
Notice both answers equal 557,728

With that explanation out of the way, let's continue. Next, we take the number 557,728 and divide it by 2:

557,728 ÷ 2 = 278,864

If the quotient is a whole number, then 2 and 278,864 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 2 278,864 557,728
-1 -2 -278,864 -557,728

Now, we try dividing 557,728 by 3:

557,728 ÷ 3 = 185,909.3333

If the quotient is a whole number, then 3 and 185,909.3333 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 2 278,864 557,728
-1 -2 -278,864 -557,728

Let's try dividing by 4:

557,728 ÷ 4 = 139,432

If the quotient is a whole number, then 4 and 139,432 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 4 139,432 278,864 557,728
-1 -2 -4 -139,432 -278,864 557,728
Keep dividing by the next highest number until you cannot divide anymore.

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

1248162932581162324646019281,2022,4044,8089,61617,42919,23234,85869,716139,432278,864557,728
-1-2-4-8-16-29-32-58-116-232-464-601-928-1,202-2,404-4,808-9,616-17,429-19,232-34,858-69,716-139,432-278,864-557,728

More Examples

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