Q: What are the factor combinations of the number 305,730,755?

 A:
Positive:   1 x 3057307555 x 6114615111 x 2779370555 x 55587411871 x 1634052971 x 1029059355 x 3268114855 x 20581
Negative: -1 x -305730755-5 x -61146151-11 x -27793705-55 x -5558741-1871 x -163405-2971 x -102905-9355 x -32681-14855 x -20581


How do I find the factor combinations of the number 305,730,755?

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 305,730,755, 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.

1 305,730,755
-1 -305,730,755

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 305,730,755.

Example:
1 x 305,730,755 = 305,730,755
and
-1 x -305,730,755 = 305,730,755
Notice both answers equal 305,730,755

With that explanation out of the way, let's continue. Next, we take the number 305,730,755 and divide it by 2:

305,730,755 ÷ 2 = 152,865,377.5

If the quotient is a whole number, then 2 and 152,865,377.5 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:

1 305,730,755
-1 -305,730,755

Now, we try dividing 305,730,755 by 3:

305,730,755 ÷ 3 = 101,910,251.6667

If the quotient is a whole number, then 3 and 101,910,251.6667 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:

1 305,730,755
-1 -305,730,755

Let's try dividing by 4:

305,730,755 ÷ 4 = 76,432,688.75

If the quotient is a whole number, then 4 and 76,432,688.75 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:

1 305,730,755
-1 305,730,755
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551,8712,9719,35514,85520,58132,681102,905163,4055,558,74127,793,70561,146,151305,730,755
-1-5-11-55-1,871-2,971-9,355-14,855-20,581-32,681-102,905-163,405-5,558,741-27,793,705-61,146,151-305,730,755

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