Q: What are the factor combinations of the number 514,316,165?

 A:
Positive:   1 x 5143161655 x 10286323311 x 4675601555 x 9351203
Negative: -1 x -514316165-5 x -102863233-11 x -46756015-55 x -9351203


How do I find the factor combinations of the number 514,316,165?

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 514,316,165, 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.

1 514,316,165
-1 -514,316,165

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 514,316,165.

Example:
1 x 514,316,165 = 514,316,165
and
-1 x -514,316,165 = 514,316,165
Notice both answers equal 514,316,165

With that explanation out of the way, let's continue. Next, we take the number 514,316,165 and divide it by 2:

514,316,165 ÷ 2 = 257,158,082.5

If the quotient is a whole number, then 2 and 257,158,082.5 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:

1 514,316,165
-1 -514,316,165

Now, we try dividing 514,316,165 by 3:

514,316,165 ÷ 3 = 171,438,721.6667

If the quotient is a whole number, then 3 and 171,438,721.6667 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:

1 514,316,165
-1 -514,316,165

Let's try dividing by 4:

514,316,165 ÷ 4 = 128,579,041.25

If the quotient is a whole number, then 4 and 128,579,041.25 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:

1 514,316,165
-1 514,316,165
Keep dividing by the next highest number until you cannot divide anymore.

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

1511559,351,20346,756,015102,863,233514,316,165
-1-5-11-55-9,351,203-46,756,015-102,863,233-514,316,165

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