Q: What are the factor combinations of the number 304,500,301?

 A:
Positive:   1 x 3045003017 x 4350004373 x 4171237179 x 1701119511 x 5958911253 x 2430173329 x 9146913067 x 23303
Negative: -1 x -304500301-7 x -43500043-73 x -4171237-179 x -1701119-511 x -595891-1253 x -243017-3329 x -91469-13067 x -23303


How do I find the factor combinations of the number 304,500,301?

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 304,500,301, 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.

1 304,500,301
-1 -304,500,301

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 304,500,301.

Example:
1 x 304,500,301 = 304,500,301
and
-1 x -304,500,301 = 304,500,301
Notice both answers equal 304,500,301

With that explanation out of the way, let's continue. Next, we take the number 304,500,301 and divide it by 2:

304,500,301 ÷ 2 = 152,250,150.5

If the quotient is a whole number, then 2 and 152,250,150.5 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:

1 304,500,301
-1 -304,500,301

Now, we try dividing 304,500,301 by 3:

304,500,301 ÷ 3 = 101,500,100.3333

If the quotient is a whole number, then 3 and 101,500,100.3333 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:

1 304,500,301
-1 -304,500,301

Let's try dividing by 4:

304,500,301 ÷ 4 = 76,125,075.25

If the quotient is a whole number, then 4 and 76,125,075.25 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:

1 304,500,301
-1 304,500,301
Keep dividing by the next highest number until you cannot divide anymore.

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

17731795111,2533,32913,06723,30391,469243,017595,8911,701,1194,171,23743,500,043304,500,301
-1-7-73-179-511-1,253-3,329-13,067-23,303-91,469-243,017-595,891-1,701,119-4,171,237-43,500,043-304,500,301

More Examples

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