Q: What are the factor combinations of the number 300,776,180?

 A:
Positive:   1 x 3007761802 x 1503880904 x 751940455 x 6015523610 x 3007761820 x 15038809
Negative: -1 x -300776180-2 x -150388090-4 x -75194045-5 x -60155236-10 x -30077618-20 x -15038809


How do I find the factor combinations of the number 300,776,180?

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 300,776,180, 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.

1 300,776,180
-1 -300,776,180

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 300,776,180.

Example:
1 x 300,776,180 = 300,776,180
and
-1 x -300,776,180 = 300,776,180
Notice both answers equal 300,776,180

With that explanation out of the way, let's continue. Next, we take the number 300,776,180 and divide it by 2:

300,776,180 ÷ 2 = 150,388,090

If the quotient is a whole number, then 2 and 150,388,090 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 150,388,090 300,776,180
-1 -2 -150,388,090 -300,776,180

Now, we try dividing 300,776,180 by 3:

300,776,180 ÷ 3 = 100,258,726.6667

If the quotient is a whole number, then 3 and 100,258,726.6667 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 2 150,388,090 300,776,180
-1 -2 -150,388,090 -300,776,180

Let's try dividing by 4:

300,776,180 ÷ 4 = 75,194,045

If the quotient is a whole number, then 4 and 75,194,045 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 75,194,045 150,388,090 300,776,180
-1 -2 -4 -75,194,045 -150,388,090 300,776,180
Keep dividing by the next highest number until you cannot divide anymore.

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

1245102015,038,80930,077,61860,155,23675,194,045150,388,090300,776,180
-1-2-4-5-10-20-15,038,809-30,077,618-60,155,236-75,194,045-150,388,090-300,776,180

More Examples

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