Q: What are the factor combinations of the number 305,747,735?

 A:
Positive:   1 x 3057477355 x 6114954759 x 5182165295 x 1036433359 x 8516651795 x 1703332887 x 10590514435 x 21181
Negative: -1 x -305747735-5 x -61149547-59 x -5182165-295 x -1036433-359 x -851665-1795 x -170333-2887 x -105905-14435 x -21181


How do I find the factor combinations of the number 305,747,735?

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 305,747,735, 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.

1 305,747,735
-1 -305,747,735

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 305,747,735.

Example:
1 x 305,747,735 = 305,747,735
and
-1 x -305,747,735 = 305,747,735
Notice both answers equal 305,747,735

With that explanation out of the way, let's continue. Next, we take the number 305,747,735 and divide it by 2:

305,747,735 ÷ 2 = 152,873,867.5

If the quotient is a whole number, then 2 and 152,873,867.5 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:

1 305,747,735
-1 -305,747,735

Now, we try dividing 305,747,735 by 3:

305,747,735 ÷ 3 = 101,915,911.6667

If the quotient is a whole number, then 3 and 101,915,911.6667 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:

1 305,747,735
-1 -305,747,735

Let's try dividing by 4:

305,747,735 ÷ 4 = 76,436,933.75

If the quotient is a whole number, then 4 and 76,436,933.75 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:

1 305,747,735
-1 305,747,735
Keep dividing by the next highest number until you cannot divide anymore.

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

15592953591,7952,88714,43521,181105,905170,333851,6651,036,4335,182,16561,149,547305,747,735
-1-5-59-295-359-1,795-2,887-14,435-21,181-105,905-170,333-851,665-1,036,433-5,182,165-61,149,547-305,747,735

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