Q: What are the factor combinations of the number 301,103,243?

 A:
Positive:   1 x 3011032437 x 4301474943 x 7002401107 x 2814049301 x 1000343749 x 4020074601 x 654439349 x 32207
Negative: -1 x -301103243-7 x -43014749-43 x -7002401-107 x -2814049-301 x -1000343-749 x -402007-4601 x -65443-9349 x -32207


How do I find the factor combinations of the number 301,103,243?

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 301,103,243, 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.

1 301,103,243
-1 -301,103,243

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 301,103,243.

Example:
1 x 301,103,243 = 301,103,243
and
-1 x -301,103,243 = 301,103,243
Notice both answers equal 301,103,243

With that explanation out of the way, let's continue. Next, we take the number 301,103,243 and divide it by 2:

301,103,243 ÷ 2 = 150,551,621.5

If the quotient is a whole number, then 2 and 150,551,621.5 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:

1 301,103,243
-1 -301,103,243

Now, we try dividing 301,103,243 by 3:

301,103,243 ÷ 3 = 100,367,747.6667

If the quotient is a whole number, then 3 and 100,367,747.6667 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:

1 301,103,243
-1 -301,103,243

Let's try dividing by 4:

301,103,243 ÷ 4 = 75,275,810.75

If the quotient is a whole number, then 4 and 75,275,810.75 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:

1 301,103,243
-1 301,103,243
Keep dividing by the next highest number until you cannot divide anymore.

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

17431073017494,6019,34932,20765,443402,0071,000,3432,814,0497,002,40143,014,749301,103,243
-1-7-43-107-301-749-4,601-9,349-32,207-65,443-402,007-1,000,343-2,814,049-7,002,401-43,014,749-301,103,243

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