Q: What are the factor combinations of the number 513,513,049?

 A:
Positive:   1 x 5135130497 x 7335900759 x 8703611413 x 1243373
Negative: -1 x -513513049-7 x -73359007-59 x -8703611-413 x -1243373


How do I find the factor combinations of the number 513,513,049?

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 513,513,049, 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.

1 513,513,049
-1 -513,513,049

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 513,513,049.

Example:
1 x 513,513,049 = 513,513,049
and
-1 x -513,513,049 = 513,513,049
Notice both answers equal 513,513,049

With that explanation out of the way, let's continue. Next, we take the number 513,513,049 and divide it by 2:

513,513,049 ÷ 2 = 256,756,524.5

If the quotient is a whole number, then 2 and 256,756,524.5 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:

1 513,513,049
-1 -513,513,049

Now, we try dividing 513,513,049 by 3:

513,513,049 ÷ 3 = 171,171,016.3333

If the quotient is a whole number, then 3 and 171,171,016.3333 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:

1 513,513,049
-1 -513,513,049

Let's try dividing by 4:

513,513,049 ÷ 4 = 128,378,262.25

If the quotient is a whole number, then 4 and 128,378,262.25 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:

1 513,513,049
-1 513,513,049
Keep dividing by the next highest number until you cannot divide anymore.

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

17594131,243,3738,703,61173,359,007513,513,049
-1-7-59-413-1,243,373-8,703,611-73,359,007-513,513,049

More Examples

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