Q: What are the factor combinations of the number 120,505,163?

 A:
Positive:   1 x 12050516317 x 708853919 x 6342377323 x 373081349 x 3452871069 x 1127275933 x 203116631 x 18173
Negative: -1 x -120505163-17 x -7088539-19 x -6342377-323 x -373081-349 x -345287-1069 x -112727-5933 x -20311-6631 x -18173


How do I find the factor combinations of the number 120,505,163?

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 120,505,163, 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.

1 120,505,163
-1 -120,505,163

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 120,505,163.

Example:
1 x 120,505,163 = 120,505,163
and
-1 x -120,505,163 = 120,505,163
Notice both answers equal 120,505,163

With that explanation out of the way, let's continue. Next, we take the number 120,505,163 and divide it by 2:

120,505,163 ÷ 2 = 60,252,581.5

If the quotient is a whole number, then 2 and 60,252,581.5 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:

1 120,505,163
-1 -120,505,163

Now, we try dividing 120,505,163 by 3:

120,505,163 ÷ 3 = 40,168,387.6667

If the quotient is a whole number, then 3 and 40,168,387.6667 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:

1 120,505,163
-1 -120,505,163

Let's try dividing by 4:

120,505,163 ÷ 4 = 30,126,290.75

If the quotient is a whole number, then 4 and 30,126,290.75 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:

1 120,505,163
-1 120,505,163
Keep dividing by the next highest number until you cannot divide anymore.

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

117193233491,0695,9336,63118,17320,311112,727345,287373,0816,342,3777,088,539120,505,163
-1-17-19-323-349-1,069-5,933-6,631-18,173-20,311-112,727-345,287-373,081-6,342,377-7,088,539-120,505,163

More Examples

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