Q: What are the factor combinations of the number 107,256,721?

 A:
Positive:   1 x 10725672111 x 975061113 x 8250517143 x 750047461 x 2326611627 x 659235071 x 211515993 x 17897
Negative: -1 x -107256721-11 x -9750611-13 x -8250517-143 x -750047-461 x -232661-1627 x -65923-5071 x -21151-5993 x -17897


How do I find the factor combinations of the number 107,256,721?

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 107,256,721, 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.

1 107,256,721
-1 -107,256,721

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 107,256,721.

Example:
1 x 107,256,721 = 107,256,721
and
-1 x -107,256,721 = 107,256,721
Notice both answers equal 107,256,721

With that explanation out of the way, let's continue. Next, we take the number 107,256,721 and divide it by 2:

107,256,721 ÷ 2 = 53,628,360.5

If the quotient is a whole number, then 2 and 53,628,360.5 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:

1 107,256,721
-1 -107,256,721

Now, we try dividing 107,256,721 by 3:

107,256,721 ÷ 3 = 35,752,240.3333

If the quotient is a whole number, then 3 and 35,752,240.3333 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:

1 107,256,721
-1 -107,256,721

Let's try dividing by 4:

107,256,721 ÷ 4 = 26,814,180.25

If the quotient is a whole number, then 4 and 26,814,180.25 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:

1 107,256,721
-1 107,256,721
Keep dividing by the next highest number until you cannot divide anymore.

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

111131434611,6275,0715,99317,89721,15165,923232,661750,0478,250,5179,750,611107,256,721
-1-11-13-143-461-1,627-5,071-5,993-17,897-21,151-65,923-232,661-750,047-8,250,517-9,750,611-107,256,721

More Examples

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