Q: What are the factor combinations of the number 320,131,105?

 A:
Positive:   1 x 3201311055 x 640262217 x 4573301535 x 9146603739 x 4331953695 x 866395173 x 6188512377 x 25865
Negative: -1 x -320131105-5 x -64026221-7 x -45733015-35 x -9146603-739 x -433195-3695 x -86639-5173 x -61885-12377 x -25865


How do I find the factor combinations of the number 320,131,105?

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 320,131,105, 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.

1 320,131,105
-1 -320,131,105

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 320,131,105.

Example:
1 x 320,131,105 = 320,131,105
and
-1 x -320,131,105 = 320,131,105
Notice both answers equal 320,131,105

With that explanation out of the way, let's continue. Next, we take the number 320,131,105 and divide it by 2:

320,131,105 ÷ 2 = 160,065,552.5

If the quotient is a whole number, then 2 and 160,065,552.5 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:

1 320,131,105
-1 -320,131,105

Now, we try dividing 320,131,105 by 3:

320,131,105 ÷ 3 = 106,710,368.3333

If the quotient is a whole number, then 3 and 106,710,368.3333 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:

1 320,131,105
-1 -320,131,105

Let's try dividing by 4:

320,131,105 ÷ 4 = 80,032,776.25

If the quotient is a whole number, then 4 and 80,032,776.25 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:

1 320,131,105
-1 320,131,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157357393,6955,17312,37725,86561,88586,639433,1959,146,60345,733,01564,026,221320,131,105
-1-5-7-35-739-3,695-5,173-12,377-25,865-61,885-86,639-433,195-9,146,603-45,733,015-64,026,221-320,131,105

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