Q: What are the factor combinations of the number 320,103,029?

 A:
Positive:   1 x 32010302923 x 1391752373 x 438497383 x 38566631679 x 1906511909 x 1676812297 x 1393576059 x 52831
Negative: -1 x -320103029-23 x -13917523-73 x -4384973-83 x -3856663-1679 x -190651-1909 x -167681-2297 x -139357-6059 x -52831


How do I find the factor combinations of the number 320,103,029?

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 320,103,029, 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.

1 320,103,029
-1 -320,103,029

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 320,103,029.

Example:
1 x 320,103,029 = 320,103,029
and
-1 x -320,103,029 = 320,103,029
Notice both answers equal 320,103,029

With that explanation out of the way, let's continue. Next, we take the number 320,103,029 and divide it by 2:

320,103,029 ÷ 2 = 160,051,514.5

If the quotient is a whole number, then 2 and 160,051,514.5 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:

1 320,103,029
-1 -320,103,029

Now, we try dividing 320,103,029 by 3:

320,103,029 ÷ 3 = 106,701,009.6667

If the quotient is a whole number, then 3 and 106,701,009.6667 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:

1 320,103,029
-1 -320,103,029

Let's try dividing by 4:

320,103,029 ÷ 4 = 80,025,757.25

If the quotient is a whole number, then 4 and 80,025,757.25 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:

1 320,103,029
-1 320,103,029
Keep dividing by the next highest number until you cannot divide anymore.

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

12373831,6791,9092,2976,05952,831139,357167,681190,6513,856,6634,384,97313,917,523320,103,029
-1-23-73-83-1,679-1,909-2,297-6,059-52,831-139,357-167,681-190,651-3,856,663-4,384,973-13,917,523-320,103,029

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