Q: What are the factor combinations of the number 309,703,835?

 A:
Positive:   1 x 3097038355 x 619407677 x 4424340535 x 88486812251 x 1375853931 x 7878511255 x 2751715757 x 19655
Negative: -1 x -309703835-5 x -61940767-7 x -44243405-35 x -8848681-2251 x -137585-3931 x -78785-11255 x -27517-15757 x -19655


How do I find the factor combinations of the number 309,703,835?

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 309,703,835, 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.

1 309,703,835
-1 -309,703,835

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 309,703,835.

Example:
1 x 309,703,835 = 309,703,835
and
-1 x -309,703,835 = 309,703,835
Notice both answers equal 309,703,835

With that explanation out of the way, let's continue. Next, we take the number 309,703,835 and divide it by 2:

309,703,835 ÷ 2 = 154,851,917.5

If the quotient is a whole number, then 2 and 154,851,917.5 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:

1 309,703,835
-1 -309,703,835

Now, we try dividing 309,703,835 by 3:

309,703,835 ÷ 3 = 103,234,611.6667

If the quotient is a whole number, then 3 and 103,234,611.6667 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:

1 309,703,835
-1 -309,703,835

Let's try dividing by 4:

309,703,835 ÷ 4 = 77,425,958.75

If the quotient is a whole number, then 4 and 77,425,958.75 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:

1 309,703,835
-1 309,703,835
Keep dividing by the next highest number until you cannot divide anymore.

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

157352,2513,93111,25515,75719,65527,51778,785137,5858,848,68144,243,40561,940,767309,703,835
-1-5-7-35-2,251-3,931-11,255-15,757-19,655-27,517-78,785-137,585-8,848,681-44,243,405-61,940,767-309,703,835

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