Q: What are the factor combinations of the number 506,174,568?

 A:
Positive:   1 x 5061745682 x 2530872843 x 1687248564 x 1265436426 x 843624288 x 6327182112 x 4218121424 x 21090607131 x 3863928262 x 1931964393 x 1287976524 x 965982786 x 6439881048 x 4829911572 x 3219943144 x 160997
Negative: -1 x -506174568-2 x -253087284-3 x -168724856-4 x -126543642-6 x -84362428-8 x -63271821-12 x -42181214-24 x -21090607-131 x -3863928-262 x -1931964-393 x -1287976-524 x -965982-786 x -643988-1048 x -482991-1572 x -321994-3144 x -160997


How do I find the factor combinations of the number 506,174,568?

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 506,174,568, 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.

1 506,174,568
-1 -506,174,568

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 506,174,568.

Example:
1 x 506,174,568 = 506,174,568
and
-1 x -506,174,568 = 506,174,568
Notice both answers equal 506,174,568

With that explanation out of the way, let's continue. Next, we take the number 506,174,568 and divide it by 2:

506,174,568 ÷ 2 = 253,087,284

If the quotient is a whole number, then 2 and 253,087,284 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 2 253,087,284 506,174,568
-1 -2 -253,087,284 -506,174,568

Now, we try dividing 506,174,568 by 3:

506,174,568 ÷ 3 = 168,724,856

If the quotient is a whole number, then 3 and 168,724,856 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 3 168,724,856 253,087,284 506,174,568
-1 -2 -3 -168,724,856 -253,087,284 -506,174,568

Let's try dividing by 4:

506,174,568 ÷ 4 = 126,543,642

If the quotient is a whole number, then 4 and 126,543,642 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 4 126,543,642 168,724,856 253,087,284 506,174,568
-1 -2 -3 -4 -126,543,642 -168,724,856 -253,087,284 506,174,568
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812241312623935247861,0481,5723,144160,997321,994482,991643,988965,9821,287,9761,931,9643,863,92821,090,60742,181,21463,271,82184,362,428126,543,642168,724,856253,087,284506,174,568
-1-2-3-4-6-8-12-24-131-262-393-524-786-1,048-1,572-3,144-160,997-321,994-482,991-643,988-965,982-1,287,976-1,931,964-3,863,928-21,090,607-42,181,214-63,271,821-84,362,428-126,543,642-168,724,856-253,087,284-506,174,568

More Examples

Here are some more numbers to try:

506,174,566506,174,567506,174,569506,174,570
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