Q: What are the factor combinations of the number 272,641,721?

 A:
Positive:   1 x 27264172111 x 24785611103 x 2647007331 x 823691727 x 3750231133 x 2406373641 x 748817997 x 34093
Negative: -1 x -272641721-11 x -24785611-103 x -2647007-331 x -823691-727 x -375023-1133 x -240637-3641 x -74881-7997 x -34093


How do I find the factor combinations of the number 272,641,721?

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 272,641,721, 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.

1 272,641,721
-1 -272,641,721

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 272,641,721.

Example:
1 x 272,641,721 = 272,641,721
and
-1 x -272,641,721 = 272,641,721
Notice both answers equal 272,641,721

With that explanation out of the way, let's continue. Next, we take the number 272,641,721 and divide it by 2:

272,641,721 ÷ 2 = 136,320,860.5

If the quotient is a whole number, then 2 and 136,320,860.5 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:

1 272,641,721
-1 -272,641,721

Now, we try dividing 272,641,721 by 3:

272,641,721 ÷ 3 = 90,880,573.6667

If the quotient is a whole number, then 3 and 90,880,573.6667 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:

1 272,641,721
-1 -272,641,721

Let's try dividing by 4:

272,641,721 ÷ 4 = 68,160,430.25

If the quotient is a whole number, then 4 and 68,160,430.25 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:

1 272,641,721
-1 272,641,721
Keep dividing by the next highest number until you cannot divide anymore.

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

1111033317271,1333,6417,99734,09374,881240,637375,023823,6912,647,00724,785,611272,641,721
-1-11-103-331-727-1,133-3,641-7,997-34,093-74,881-240,637-375,023-823,691-2,647,007-24,785,611-272,641,721

More Examples

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