Q: What are the factor combinations of the number 273,271,019?

 A:
Positive:   1 x 2732710197 x 3903871747 x 581427797 x 2817227329 x 830611679 x 4024614559 x 599418563 x 31913
Negative: -1 x -273271019-7 x -39038717-47 x -5814277-97 x -2817227-329 x -830611-679 x -402461-4559 x -59941-8563 x -31913


How do I find the factor combinations of the number 273,271,019?

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 273,271,019, 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.

1 273,271,019
-1 -273,271,019

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 273,271,019.

Example:
1 x 273,271,019 = 273,271,019
and
-1 x -273,271,019 = 273,271,019
Notice both answers equal 273,271,019

With that explanation out of the way, let's continue. Next, we take the number 273,271,019 and divide it by 2:

273,271,019 ÷ 2 = 136,635,509.5

If the quotient is a whole number, then 2 and 136,635,509.5 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:

1 273,271,019
-1 -273,271,019

Now, we try dividing 273,271,019 by 3:

273,271,019 ÷ 3 = 91,090,339.6667

If the quotient is a whole number, then 3 and 91,090,339.6667 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:

1 273,271,019
-1 -273,271,019

Let's try dividing by 4:

273,271,019 ÷ 4 = 68,317,754.75

If the quotient is a whole number, then 4 and 68,317,754.75 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:

1 273,271,019
-1 273,271,019
Keep dividing by the next highest number until you cannot divide anymore.

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

1747973296794,5598,56331,91359,941402,461830,6112,817,2275,814,27739,038,717273,271,019
-1-7-47-97-329-679-4,559-8,563-31,913-59,941-402,461-830,611-2,817,227-5,814,277-39,038,717-273,271,019

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