Q: What are the factor combinations of the number 300,356,045?

 A:
Positive:   1 x 3003560455 x 6007120911 x 2730509529 x 1035710555 x 5461019145 x 2071421319 x 9415551595 x 188311
Negative: -1 x -300356045-5 x -60071209-11 x -27305095-29 x -10357105-55 x -5461019-145 x -2071421-319 x -941555-1595 x -188311


How do I find the factor combinations of the number 300,356,045?

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 300,356,045, 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.

1 300,356,045
-1 -300,356,045

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 300,356,045.

Example:
1 x 300,356,045 = 300,356,045
and
-1 x -300,356,045 = 300,356,045
Notice both answers equal 300,356,045

With that explanation out of the way, let's continue. Next, we take the number 300,356,045 and divide it by 2:

300,356,045 ÷ 2 = 150,178,022.5

If the quotient is a whole number, then 2 and 150,178,022.5 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:

1 300,356,045
-1 -300,356,045

Now, we try dividing 300,356,045 by 3:

300,356,045 ÷ 3 = 100,118,681.6667

If the quotient is a whole number, then 3 and 100,118,681.6667 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:

1 300,356,045
-1 -300,356,045

Let's try dividing by 4:

300,356,045 ÷ 4 = 75,089,011.25

If the quotient is a whole number, then 4 and 75,089,011.25 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:

1 300,356,045
-1 300,356,045
Keep dividing by the next highest number until you cannot divide anymore.

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

151129551453191,595188,311941,5552,071,4215,461,01910,357,10527,305,09560,071,209300,356,045
-1-5-11-29-55-145-319-1,595-188,311-941,555-2,071,421-5,461,019-10,357,105-27,305,095-60,071,209-300,356,045

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