Q: What are the factor combinations of the number 524,406,509?

 A:
Positive:   1 x 52440650911 x 4767331923 x 2280028331 x 16916339253 x 2072753341 x 1537849713 x 7354937843 x 66863
Negative: -1 x -524406509-11 x -47673319-23 x -22800283-31 x -16916339-253 x -2072753-341 x -1537849-713 x -735493-7843 x -66863


How do I find the factor combinations of the number 524,406,509?

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 524,406,509, 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.

1 524,406,509
-1 -524,406,509

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 524,406,509.

Example:
1 x 524,406,509 = 524,406,509
and
-1 x -524,406,509 = 524,406,509
Notice both answers equal 524,406,509

With that explanation out of the way, let's continue. Next, we take the number 524,406,509 and divide it by 2:

524,406,509 ÷ 2 = 262,203,254.5

If the quotient is a whole number, then 2 and 262,203,254.5 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:

1 524,406,509
-1 -524,406,509

Now, we try dividing 524,406,509 by 3:

524,406,509 ÷ 3 = 174,802,169.6667

If the quotient is a whole number, then 3 and 174,802,169.6667 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:

1 524,406,509
-1 -524,406,509

Let's try dividing by 4:

524,406,509 ÷ 4 = 131,101,627.25

If the quotient is a whole number, then 4 and 131,101,627.25 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:

1 524,406,509
-1 524,406,509
Keep dividing by the next highest number until you cannot divide anymore.

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

11123312533417137,84366,863735,4931,537,8492,072,75316,916,33922,800,28347,673,319524,406,509
-1-11-23-31-253-341-713-7,843-66,863-735,493-1,537,849-2,072,753-16,916,339-22,800,283-47,673,319-524,406,509

More Examples

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