Q: What are the factor combinations of the number 302,231,305?

 A:
Positive:   1 x 3022313055 x 6044626143 x 702863567 x 4510915215 x 1405727335 x 9021832881 x 10490514405 x 20981
Negative: -1 x -302231305-5 x -60446261-43 x -7028635-67 x -4510915-215 x -1405727-335 x -902183-2881 x -104905-14405 x -20981


How do I find the factor combinations of the number 302,231,305?

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 302,231,305, 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.

1 302,231,305
-1 -302,231,305

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 302,231,305.

Example:
1 x 302,231,305 = 302,231,305
and
-1 x -302,231,305 = 302,231,305
Notice both answers equal 302,231,305

With that explanation out of the way, let's continue. Next, we take the number 302,231,305 and divide it by 2:

302,231,305 ÷ 2 = 151,115,652.5

If the quotient is a whole number, then 2 and 151,115,652.5 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:

1 302,231,305
-1 -302,231,305

Now, we try dividing 302,231,305 by 3:

302,231,305 ÷ 3 = 100,743,768.3333

If the quotient is a whole number, then 3 and 100,743,768.3333 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:

1 302,231,305
-1 -302,231,305

Let's try dividing by 4:

302,231,305 ÷ 4 = 75,557,826.25

If the quotient is a whole number, then 4 and 75,557,826.25 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:

1 302,231,305
-1 302,231,305
Keep dividing by the next highest number until you cannot divide anymore.

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

1543672153352,88114,40520,981104,905902,1831,405,7274,510,9157,028,63560,446,261302,231,305
-1-5-43-67-215-335-2,881-14,405-20,981-104,905-902,183-1,405,727-4,510,915-7,028,635-60,446,261-302,231,305

More Examples

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