Q: What are the factor combinations of the number 300,444,305?

 A:
Positive:   1 x 3004443055 x 600888617 x 4292061535 x 8584123103 x 2916935515 x 583387721 x 4167053605 x 83341
Negative: -1 x -300444305-5 x -60088861-7 x -42920615-35 x -8584123-103 x -2916935-515 x -583387-721 x -416705-3605 x -83341


How do I find the factor combinations of the number 300,444,305?

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 300,444,305, 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.

1 300,444,305
-1 -300,444,305

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 300,444,305.

Example:
1 x 300,444,305 = 300,444,305
and
-1 x -300,444,305 = 300,444,305
Notice both answers equal 300,444,305

With that explanation out of the way, let's continue. Next, we take the number 300,444,305 and divide it by 2:

300,444,305 ÷ 2 = 150,222,152.5

If the quotient is a whole number, then 2 and 150,222,152.5 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:

1 300,444,305
-1 -300,444,305

Now, we try dividing 300,444,305 by 3:

300,444,305 ÷ 3 = 100,148,101.6667

If the quotient is a whole number, then 3 and 100,148,101.6667 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:

1 300,444,305
-1 -300,444,305

Let's try dividing by 4:

300,444,305 ÷ 4 = 75,111,076.25

If the quotient is a whole number, then 4 and 75,111,076.25 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:

1 300,444,305
-1 300,444,305
Keep dividing by the next highest number until you cannot divide anymore.

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

157351035157213,60583,341416,705583,3872,916,9358,584,12342,920,61560,088,861300,444,305
-1-5-7-35-103-515-721-3,605-83,341-416,705-583,387-2,916,935-8,584,123-42,920,615-60,088,861-300,444,305

More Examples

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