Q: What are the factor combinations of the number 304,400,311?

 A:
Positive:   1 x 30440031119 x 1602106943 x 7079077229 x 1329259817 x 3725831627 x 1870934351 x 699619847 x 30913
Negative: -1 x -304400311-19 x -16021069-43 x -7079077-229 x -1329259-817 x -372583-1627 x -187093-4351 x -69961-9847 x -30913


How do I find the factor combinations of the number 304,400,311?

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 304,400,311, 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.

1 304,400,311
-1 -304,400,311

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 304,400,311.

Example:
1 x 304,400,311 = 304,400,311
and
-1 x -304,400,311 = 304,400,311
Notice both answers equal 304,400,311

With that explanation out of the way, let's continue. Next, we take the number 304,400,311 and divide it by 2:

304,400,311 ÷ 2 = 152,200,155.5

If the quotient is a whole number, then 2 and 152,200,155.5 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:

1 304,400,311
-1 -304,400,311

Now, we try dividing 304,400,311 by 3:

304,400,311 ÷ 3 = 101,466,770.3333

If the quotient is a whole number, then 3 and 101,466,770.3333 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:

1 304,400,311
-1 -304,400,311

Let's try dividing by 4:

304,400,311 ÷ 4 = 76,100,077.75

If the quotient is a whole number, then 4 and 76,100,077.75 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:

1 304,400,311
-1 304,400,311
Keep dividing by the next highest number until you cannot divide anymore.

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

119432298171,6274,3519,84730,91369,961187,093372,5831,329,2597,079,07716,021,069304,400,311
-1-19-43-229-817-1,627-4,351-9,847-30,913-69,961-187,093-372,583-1,329,259-7,079,077-16,021,069-304,400,311

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