Q: What are the factor combinations of the number 260,448,721?

 A:
Positive:   1 x 26044872113 x 2003451717 x 1532051343 x 6056947221 x 1178501559 x 465919731 x 3562919503 x 27407
Negative: -1 x -260448721-13 x -20034517-17 x -15320513-43 x -6056947-221 x -1178501-559 x -465919-731 x -356291-9503 x -27407


How do I find the factor combinations of the number 260,448,721?

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 260,448,721, 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.

1 260,448,721
-1 -260,448,721

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 260,448,721.

Example:
1 x 260,448,721 = 260,448,721
and
-1 x -260,448,721 = 260,448,721
Notice both answers equal 260,448,721

With that explanation out of the way, let's continue. Next, we take the number 260,448,721 and divide it by 2:

260,448,721 ÷ 2 = 130,224,360.5

If the quotient is a whole number, then 2 and 130,224,360.5 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:

1 260,448,721
-1 -260,448,721

Now, we try dividing 260,448,721 by 3:

260,448,721 ÷ 3 = 86,816,240.3333

If the quotient is a whole number, then 3 and 86,816,240.3333 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:

1 260,448,721
-1 -260,448,721

Let's try dividing by 4:

260,448,721 ÷ 4 = 65,112,180.25

If the quotient is a whole number, then 4 and 65,112,180.25 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:

1 260,448,721
-1 260,448,721
Keep dividing by the next highest number until you cannot divide anymore.

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

11317432215597319,50327,407356,291465,9191,178,5016,056,94715,320,51320,034,517260,448,721
-1-13-17-43-221-559-731-9,503-27,407-356,291-465,919-1,178,501-6,056,947-15,320,513-20,034,517-260,448,721

More Examples

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