Q: What are the factor combinations of the number 108,004,721?

 A:
Positive:   1 x 10800472111 x 981861119 x 5684459109 x 990869121 x 892601209 x 516769431 x 2505911199 x 900792071 x 521512299 x 469794741 x 227818189 x 13189
Negative: -1 x -108004721-11 x -9818611-19 x -5684459-109 x -990869-121 x -892601-209 x -516769-431 x -250591-1199 x -90079-2071 x -52151-2299 x -46979-4741 x -22781-8189 x -13189


How do I find the factor combinations of the number 108,004,721?

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 108,004,721, 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.

1 108,004,721
-1 -108,004,721

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 108,004,721.

Example:
1 x 108,004,721 = 108,004,721
and
-1 x -108,004,721 = 108,004,721
Notice both answers equal 108,004,721

With that explanation out of the way, let's continue. Next, we take the number 108,004,721 and divide it by 2:

108,004,721 ÷ 2 = 54,002,360.5

If the quotient is a whole number, then 2 and 54,002,360.5 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:

1 108,004,721
-1 -108,004,721

Now, we try dividing 108,004,721 by 3:

108,004,721 ÷ 3 = 36,001,573.6667

If the quotient is a whole number, then 3 and 36,001,573.6667 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:

1 108,004,721
-1 -108,004,721

Let's try dividing by 4:

108,004,721 ÷ 4 = 27,001,180.25

If the quotient is a whole number, then 4 and 27,001,180.25 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:

1 108,004,721
-1 108,004,721
Keep dividing by the next highest number until you cannot divide anymore.

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

111191091212094311,1992,0712,2994,7418,18913,18922,78146,97952,15190,079250,591516,769892,601990,8695,684,4599,818,611108,004,721
-1-11-19-109-121-209-431-1,199-2,071-2,299-4,741-8,189-13,189-22,781-46,979-52,151-90,079-250,591-516,769-892,601-990,869-5,684,459-9,818,611-108,004,721

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