Q: What are the factor combinations of the number 303,812,369?

 A:
Positive:   1 x 3038123697 x 4340176731 x 9800399217 x 1400057461 x 6590293037 x 1000373227 x 9414714291 x 21259
Negative: -1 x -303812369-7 x -43401767-31 x -9800399-217 x -1400057-461 x -659029-3037 x -100037-3227 x -94147-14291 x -21259


How do I find the factor combinations of the number 303,812,369?

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 303,812,369, 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.

1 303,812,369
-1 -303,812,369

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 303,812,369.

Example:
1 x 303,812,369 = 303,812,369
and
-1 x -303,812,369 = 303,812,369
Notice both answers equal 303,812,369

With that explanation out of the way, let's continue. Next, we take the number 303,812,369 and divide it by 2:

303,812,369 ÷ 2 = 151,906,184.5

If the quotient is a whole number, then 2 and 151,906,184.5 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:

1 303,812,369
-1 -303,812,369

Now, we try dividing 303,812,369 by 3:

303,812,369 ÷ 3 = 101,270,789.6667

If the quotient is a whole number, then 3 and 101,270,789.6667 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:

1 303,812,369
-1 -303,812,369

Let's try dividing by 4:

303,812,369 ÷ 4 = 75,953,092.25

If the quotient is a whole number, then 4 and 75,953,092.25 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:

1 303,812,369
-1 303,812,369
Keep dividing by the next highest number until you cannot divide anymore.

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

17312174613,0373,22714,29121,25994,147100,037659,0291,400,0579,800,39943,401,767303,812,369
-1-7-31-217-461-3,037-3,227-14,291-21,259-94,147-100,037-659,029-1,400,057-9,800,399-43,401,767-303,812,369

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