Q: What are the factor combinations of the number 565,296?

 A:
Positive:   1 x 5652962 x 2826483 x 1884324 x 1413246 x 942168 x 7066212 x 4710816 x 3533124 x 2355448 x 11777
Negative: -1 x -565296-2 x -282648-3 x -188432-4 x -141324-6 x -94216-8 x -70662-12 x -47108-16 x -35331-24 x -23554-48 x -11777


How do I find the factor combinations of the number 565,296?

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 565,296, 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.

1 565,296
-1 -565,296

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 565,296.

Example:
1 x 565,296 = 565,296
and
-1 x -565,296 = 565,296
Notice both answers equal 565,296

With that explanation out of the way, let's continue. Next, we take the number 565,296 and divide it by 2:

565,296 ÷ 2 = 282,648

If the quotient is a whole number, then 2 and 282,648 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 2 282,648 565,296
-1 -2 -282,648 -565,296

Now, we try dividing 565,296 by 3:

565,296 ÷ 3 = 188,432

If the quotient is a whole number, then 3 and 188,432 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 3 188,432 282,648 565,296
-1 -2 -3 -188,432 -282,648 -565,296

Let's try dividing by 4:

565,296 ÷ 4 = 141,324

If the quotient is a whole number, then 4 and 141,324 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 3 4 141,324 188,432 282,648 565,296
-1 -2 -3 -4 -141,324 -188,432 -282,648 565,296
Keep dividing by the next highest number until you cannot divide anymore.

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

1234681216244811,77723,55435,33147,10870,66294,216141,324188,432282,648565,296
-1-2-3-4-6-8-12-16-24-48-11,777-23,554-35,331-47,108-70,662-94,216-141,324-188,432-282,648-565,296

More Examples

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