Q: What are the factor combinations of the number 300,114,367?

 A:
Positive:   1 x 3001143677 x 4287348119 x 1579549349 x 6124783133 x 2256499343 x 874969931 x 3223576517 x 46051
Negative: -1 x -300114367-7 x -42873481-19 x -15795493-49 x -6124783-133 x -2256499-343 x -874969-931 x -322357-6517 x -46051


How do I find the factor combinations of the number 300,114,367?

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 300,114,367, 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.

1 300,114,367
-1 -300,114,367

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 300,114,367.

Example:
1 x 300,114,367 = 300,114,367
and
-1 x -300,114,367 = 300,114,367
Notice both answers equal 300,114,367

With that explanation out of the way, let's continue. Next, we take the number 300,114,367 and divide it by 2:

300,114,367 ÷ 2 = 150,057,183.5

If the quotient is a whole number, then 2 and 150,057,183.5 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:

1 300,114,367
-1 -300,114,367

Now, we try dividing 300,114,367 by 3:

300,114,367 ÷ 3 = 100,038,122.3333

If the quotient is a whole number, then 3 and 100,038,122.3333 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:

1 300,114,367
-1 -300,114,367

Let's try dividing by 4:

300,114,367 ÷ 4 = 75,028,591.75

If the quotient is a whole number, then 4 and 75,028,591.75 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:

1 300,114,367
-1 300,114,367
Keep dividing by the next highest number until you cannot divide anymore.

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

1719491333439316,51746,051322,357874,9692,256,4996,124,78315,795,49342,873,481300,114,367
-1-7-19-49-133-343-931-6,517-46,051-322,357-874,969-2,256,499-6,124,783-15,795,493-42,873,481-300,114,367

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