Q: What are the factor combinations of the number 514,136,029?

 A:
Positive:   1 x 51413602911 x 4673963919 x 2705979179 x 6508051209 x 2459981869 x 5916411501 x 34252916511 x 31139
Negative: -1 x -514136029-11 x -46739639-19 x -27059791-79 x -6508051-209 x -2459981-869 x -591641-1501 x -342529-16511 x -31139


How do I find the factor combinations of the number 514,136,029?

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 514,136,029, 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.

1 514,136,029
-1 -514,136,029

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 514,136,029.

Example:
1 x 514,136,029 = 514,136,029
and
-1 x -514,136,029 = 514,136,029
Notice both answers equal 514,136,029

With that explanation out of the way, let's continue. Next, we take the number 514,136,029 and divide it by 2:

514,136,029 ÷ 2 = 257,068,014.5

If the quotient is a whole number, then 2 and 257,068,014.5 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:

1 514,136,029
-1 -514,136,029

Now, we try dividing 514,136,029 by 3:

514,136,029 ÷ 3 = 171,378,676.3333

If the quotient is a whole number, then 3 and 171,378,676.3333 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:

1 514,136,029
-1 -514,136,029

Let's try dividing by 4:

514,136,029 ÷ 4 = 128,534,007.25

If the quotient is a whole number, then 4 and 128,534,007.25 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:

1 514,136,029
-1 514,136,029
Keep dividing by the next highest number until you cannot divide anymore.

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

11119792098691,50116,51131,139342,529591,6412,459,9816,508,05127,059,79146,739,639514,136,029
-1-11-19-79-209-869-1,501-16,511-31,139-342,529-591,641-2,459,981-6,508,051-27,059,791-46,739,639-514,136,029

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