Q: What are the factor combinations of the number 303,123,073?

 A:
Positive:   1 x 30312307311 x 2755664317 x 17830769187 x 1620979457 x 6632893547 x 854595027 x 602997769 x 39017
Negative: -1 x -303123073-11 x -27556643-17 x -17830769-187 x -1620979-457 x -663289-3547 x -85459-5027 x -60299-7769 x -39017


How do I find the factor combinations of the number 303,123,073?

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 303,123,073, 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.

1 303,123,073
-1 -303,123,073

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 303,123,073.

Example:
1 x 303,123,073 = 303,123,073
and
-1 x -303,123,073 = 303,123,073
Notice both answers equal 303,123,073

With that explanation out of the way, let's continue. Next, we take the number 303,123,073 and divide it by 2:

303,123,073 ÷ 2 = 151,561,536.5

If the quotient is a whole number, then 2 and 151,561,536.5 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:

1 303,123,073
-1 -303,123,073

Now, we try dividing 303,123,073 by 3:

303,123,073 ÷ 3 = 101,041,024.3333

If the quotient is a whole number, then 3 and 101,041,024.3333 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:

1 303,123,073
-1 -303,123,073

Let's try dividing by 4:

303,123,073 ÷ 4 = 75,780,768.25

If the quotient is a whole number, then 4 and 75,780,768.25 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:

1 303,123,073
-1 303,123,073
Keep dividing by the next highest number until you cannot divide anymore.

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

111171874573,5475,0277,76939,01760,29985,459663,2891,620,97917,830,76927,556,643303,123,073
-1-11-17-187-457-3,547-5,027-7,769-39,017-60,299-85,459-663,289-1,620,979-17,830,769-27,556,643-303,123,073

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